/*
 * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED 
 * All rights reserved.
 * 
 * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a ligfsted,
 * non-exclusive and royalty-free license to use, copy, modify and
 * redistribute, solely for non-commercial and non-profit purposes, the
 * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
 * conditions of this Agreement. For the avoidance of doubt, you acquire
 * only a ligfsted right to use the SOFTWARE hereunder, and FLL or any
 * third party developer retains all rights, including but not ligfsted to
 * copyrights, in and to the SOFTWARE.
 * 
 * (1) FLL does not grant you a license in any way for commercial
 * purposes. You may use the SOFTWARE only for non-commercial and
 * non-profit purposes only, such as acadegfsc, research and internal
 * business use.
 * (2) The SOFTWARE is protected by the Copyright Law of Japan and
 * international copyright treaties. If you make copies of the SOFTWARE,
 * with or without modification, as pergfstted hereunder, you shall affix
 * to all such copies of the SOFTWARE the above copyright notice.
 * (3) An explicit reference to this SOFTWARE and its copyright owner
 * shall be made on your publication or presentation in any form of the
 * results obtained by use of the SOFTWARE.
 * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
 * e-mail at risa-adgfsn@sec.flab.fujitsu.co.jp of the detailed specification
 * for such modification or the source code of the modified part of the
 * SOFTWARE.
 * 
 * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
 * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
 * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
 * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
 * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
 * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
 * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
 * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
 * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
 * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
 * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
 * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
 * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
 * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
 * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
 * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
 * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
 *
 * $OpenXM: OpenXM_contrib2/asir2018/engine/gfs.c,v 1.2 2018/09/28 08:20:28 noro Exp $
*/
#include "ca.h"
#include "inline.h"

/* q = p^n */

P current_gfs_ext;
int current_gfs_p;
int current_gfs_q;
int current_gfs_q1;
int *current_gfs_plus1;
int *current_gfs_ntoi;
int *current_gfs_iton;

struct prim_root_info {
  int p;
  int extdeg;
  int defpoly;
  int prim_root;
};

/* if p >= SF_THRESHOLD, usual representation is used */

#define SF_THRESHOLD 16384

struct prim_root_info prim_root_info_tab[] = {
{2,1,0,0}, {2,2,7,2}, {2,3,11,2}, {2,4,19,2}, {2,5,37,2}, {2,6,67,2},
{2,7,131,2}, {2,8,283,3}, {2,9,515,7}, {2,10,1033,2}, {2,11,2053,2},
{2,12,4105,3}, {2,13,8219,2}, {2,14,16417,7}, {2,15,32771,2}, {3,1,0,2},
{3,2,10,4}, {3,3,34,3}, {3,4,86,3}, {3,5,250,3}, {3,6,734,3}, {3,7,2198,5},
{3,8,6572,38}, {3,9,19747,3}, {3,10,59068,34}, {5,1,0,2}, {5,2,27,6},
{5,3,131,9}, {5,4,627,6}, {5,5,3146,10}, {5,6,15632,5}, {7,1,0,3},
{7,2,50,9}, {7,3,345,22}, {7,4,2409,12}, {7,5,16817,9}, {11,1,0,2},
{11,2,122,15}, {11,3,1346,11}, {11,4,14654,11}, {13,1,0,2}, {13,2,171,15},
{13,3,2199,15}, {13,4,28563,17}, {17,1,0,3}, {17,2,292,19}, {17,3,4933,17},
{19,1,0,2}, {19,2,362,22}, {19,3,6861,29}, {23,1,0,5}, {23,2,530,25},
{23,3,12193,23}, {29,1,0,2}, {29,2,843,30}, {29,3,24422,30}, {31,1,0,3},
{31,2,962,35}, {31,3,29794,34}, {37,1,0,2}, {37,2,1371,41}, {37,3,50655,75},
{41,1,0,6}, {41,2,1684,43}, {43,1,0,3}, {43,2,1850,45}, {47,1,0,5},
{47,2,2210,49}, {53,1,0,2}, {53,2,2811,54}, {59,1,0,2}, {59,2,3482,62},
{61,1,0,2}, {61,2,3723,63}, {67,1,0,2}, {67,2,4490,74}, {71,1,0,7},
{71,2,5042,79}, {73,1,0,5}, {73,2,5334,76}, {79,1,0,3}, {79,2,6242,85},
{83,1,0,2}, {83,2,6890,93}, {89,1,0,3}, {89,2,7924,91}, {97,1,0,5},
{97,2,9414,101}, {101,1,0,2}, {101,2,10203,102}, 
{103,1,0,5}, {103,2,10610,105}, {107,1,0,2}, {107,2,11450,109}, 
{109,1,0,6}, {109,2,11883,111}, {113,1,0,3}, {113,2,12772,117}, 
{127,1,0,3}, {127,2,16130,135}, {131,1,0,2}, {131,2,17162,134},
{137,1,0,3}, {137,2,18772,145}, {139,1,0,2}, {139,2,19322,143}, 
{149,1,0,2}, {149,2,22203,152}, {151,1,0,6}, {151,2,22802,160}, 
{157,1,0,5}, {157,2,24651,159}, {163,1,0,2}, {163,2,26570,170}, 
{167,1,0,5}, {167,2,27890,169}, {173,1,0,2}, {173,2,29931,174}, 
{179,1,0,2}, {179,2,32042,182}, {181,1,0,2}, {181,2,32763,185}, 
{191,1,0,19}, {191,2,36482,201}, {193,1,0,5}, {193,2,37254,198}, 
{197,1,0,2}, {197,2,38811,200}, {199,1,0,3}, {199,2,39602,212}, 
{211,1,0,2}, {211,2,44522,215}, {223,1,0,3}, {223,2,49730,225}, 
{227,1,0,2}, {227,2,51530,229}, {229,1,0,6}, {229,2,52443,231}, 
{233,1,0,3}, {233,2,54292,241}, {239,1,0,7}, {239,2,57122,247},
{241,1,0,7}, {241,2,58088,248}, {251,1,0,6}, {251,2,63002,256}, 
{257,1,0,3}, {263,1,0,5}, {269,1,0,2}, {271,1,0,6}, {277,1,0,5}, {281,1,0,3},
{283,1,0,3}, {293,1,0,2}, {307,1,0,5}, {311,1,0,17}, {313,1,0,10},
{317,1,0,2}, {331,1,0,3}, {337,1,0,10}, {347,1,0,2}, {349,1,0,2},
{353,1,0,3}, {359,1,0,7}, {367,1,0,6}, {373,1,0,2}, {379,1,0,2},
{383,1,0,5}, {389,1,0,2}, {397,1,0,5}, {401,1,0,3}, {409,1,0,21},
{419,1,0,2}, {421,1,0,2}, {431,1,0,7}, {433,1,0,5}, {439,1,0,15},
{443,1,0,2}, {449,1,0,3}, {457,1,0,13}, {461,1,0,2}, {463,1,0,3},
{467,1,0,2}, {479,1,0,13}, {487,1,0,3}, {491,1,0,2}, {499,1,0,7},
{503,1,0,5}, {509,1,0,2}, {521,1,0,3}, {523,1,0,2}, {541,1,0,2},
{547,1,0,2}, {557,1,0,2}, {563,1,0,2}, {569,1,0,3}, {571,1,0,3},
{577,1,0,5}, {587,1,0,2}, {593,1,0,3}, {599,1,0,7}, {601,1,0,7},
{607,1,0,3}, {613,1,0,2}, {617,1,0,3}, {619,1,0,2}, {631,1,0,3},
{641,1,0,3}, {643,1,0,11}, {647,1,0,5}, {653,1,0,2}, {659,1,0,2},
{661,1,0,2}, {673,1,0,5}, {677,1,0,2}, {683,1,0,5}, {691,1,0,3},
{701,1,0,2}, {709,1,0,2}, {719,1,0,11}, {727,1,0,5}, {733,1,0,6},
{739,1,0,3}, {743,1,0,5}, {751,1,0,3}, {757,1,0,2}, {761,1,0,6},
{769,1,0,11}, {773,1,0,2}, {787,1,0,2}, {797,1,0,2}, {809,1,0,3},
{811,1,0,3}, {821,1,0,2}, {823,1,0,3}, {827,1,0,2}, {829,1,0,2},
{839,1,0,11}, {853,1,0,2}, {857,1,0,3}, {859,1,0,2}, {863,1,0,5},
{877,1,0,2}, {881,1,0,3}, {883,1,0,2}, {887,1,0,5}, {907,1,0,2},
{911,1,0,17}, {919,1,0,7}, {929,1,0,3}, {937,1,0,5}, {941,1,0,2},
{947,1,0,2}, {953,1,0,3}, {967,1,0,5}, {971,1,0,6}, {977,1,0,3},
{983,1,0,5}, {991,1,0,6}, {997,1,0,7}, {1009,1,0,11}, {1013,1,0,3},
{1019,1,0,2}, {1021,1,0,10}, {1031,1,0,14}, {1033,1,0,5}, {1039,1,0,3},
{1049,1,0,3}, {1051,1,0,7}, {1061,1,0,2}, {1063,1,0,3}, {1069,1,0,6},
{1087,1,0,3}, {1091,1,0,2}, {1093,1,0,5}, {1097,1,0,3}, {1103,1,0,5},
{1109,1,0,2}, {1117,1,0,2}, {1123,1,0,2}, {1129,1,0,11}, {1151,1,0,17},
{1153,1,0,5}, {1163,1,0,5}, {1171,1,0,2}, {1181,1,0,7}, {1187,1,0,2},
{1193,1,0,3}, {1201,1,0,11}, {1213,1,0,2}, {1217,1,0,3}, {1223,1,0,5},
{1229,1,0,2}, {1231,1,0,3}, {1237,1,0,2}, {1249,1,0,7}, {1259,1,0,2},
{1277,1,0,2}, {1279,1,0,3}, {1283,1,0,2}, {1289,1,0,6}, {1291,1,0,2},
{1297,1,0,10}, {1301,1,0,2}, {1303,1,0,6}, {1307,1,0,2}, {1319,1,0,13},
{1321,1,0,13}, {1327,1,0,3}, {1361,1,0,3}, {1367,1,0,5}, {1373,1,0,2},
{1381,1,0,2}, {1399,1,0,13}, {1409,1,0,3}, {1423,1,0,3}, {1427,1,0,2},
{1429,1,0,6}, {1433,1,0,3}, {1439,1,0,7}, {1447,1,0,3}, {1451,1,0,2},
{1453,1,0,2}, {1459,1,0,3}, {1471,1,0,6}, {1481,1,0,3}, {1483,1,0,2},
{1487,1,0,5}, {1489,1,0,14}, {1493,1,0,2}, {1499,1,0,2}, {1511,1,0,11},
{1523,1,0,2}, {1531,1,0,2}, {1543,1,0,5}, {1549,1,0,2}, {1553,1,0,3},
{1559,1,0,19}, {1567,1,0,3}, {1571,1,0,2}, {1579,1,0,3}, {1583,1,0,5},
{1597,1,0,11}, {1601,1,0,3}, {1607,1,0,5}, {1609,1,0,7}, {1613,1,0,3},
{1619,1,0,2}, {1621,1,0,2}, {1627,1,0,3}, {1637,1,0,2}, {1657,1,0,11},
{1663,1,0,3}, {1667,1,0,2}, {1669,1,0,2}, {1693,1,0,2}, {1697,1,0,3},
{1699,1,0,3}, {1709,1,0,3}, {1721,1,0,3}, {1723,1,0,3}, {1733,1,0,2},
{1741,1,0,2}, {1747,1,0,2}, {1753,1,0,7}, {1759,1,0,6}, {1777,1,0,5},
{1783,1,0,10}, {1787,1,0,2}, {1789,1,0,6}, {1801,1,0,11}, {1811,1,0,6},
{1823,1,0,5}, {1831,1,0,3}, {1847,1,0,5}, {1861,1,0,2}, {1867,1,0,2},
{1871,1,0,14}, {1873,1,0,10}, {1877,1,0,2}, {1879,1,0,6}, {1889,1,0,3},
{1901,1,0,2}, {1907,1,0,2}, {1913,1,0,3}, {1931,1,0,2}, {1933,1,0,5},
{1949,1,0,2}, {1951,1,0,3}, {1973,1,0,2}, {1979,1,0,2}, {1987,1,0,2},
{1993,1,0,5}, {1997,1,0,2}, {1999,1,0,3}, {2003,1,0,5}, {2011,1,0,3},
{2017,1,0,5}, {2027,1,0,2}, {2029,1,0,2}, {2039,1,0,7}, {2053,1,0,2},
{2063,1,0,5}, {2069,1,0,2}, {2081,1,0,3}, {2083,1,0,2}, {2087,1,0,5},
{2089,1,0,7}, {2099,1,0,2}, {2111,1,0,7}, {2113,1,0,5}, {2129,1,0,3},
{2131,1,0,2}, {2137,1,0,10}, {2141,1,0,2}, {2143,1,0,3}, {2153,1,0,3},
{2161,1,0,23}, {2179,1,0,7}, {2203,1,0,5}, {2207,1,0,5}, {2213,1,0,2},
{2221,1,0,2}, {2237,1,0,2}, {2239,1,0,3}, {2243,1,0,2}, {2251,1,0,7},
{2267,1,0,2}, {2269,1,0,2}, {2273,1,0,3}, {2281,1,0,7}, {2287,1,0,19},
{2293,1,0,2}, {2297,1,0,5}, {2309,1,0,2}, {2311,1,0,3}, {2333,1,0,2},
{2339,1,0,2}, {2341,1,0,7}, {2347,1,0,3}, {2351,1,0,13}, {2357,1,0,2},
{2371,1,0,2}, {2377,1,0,5}, {2381,1,0,3}, {2383,1,0,5}, {2389,1,0,2},
{2393,1,0,3}, {2399,1,0,11}, {2411,1,0,6}, {2417,1,0,3}, {2423,1,0,5},
{2437,1,0,2}, {2441,1,0,6}, {2447,1,0,5}, {2459,1,0,2}, {2467,1,0,2},
{2473,1,0,5}, {2477,1,0,2}, {2503,1,0,3}, {2521,1,0,17}, {2531,1,0,2},
{2539,1,0,2}, {2543,1,0,5}, {2549,1,0,2}, {2551,1,0,6}, {2557,1,0,2},
{2579,1,0,2}, {2591,1,0,7}, {2593,1,0,7}, {2609,1,0,3}, {2617,1,0,5},
{2621,1,0,2}, {2633,1,0,3}, {2647,1,0,3}, {2657,1,0,3}, {2659,1,0,2},
{2663,1,0,5}, {2671,1,0,7}, {2677,1,0,2}, {2683,1,0,2}, {2687,1,0,5},
{2689,1,0,19}, {2693,1,0,2}, {2699,1,0,2}, {2707,1,0,2}, {2711,1,0,7},
{2713,1,0,5}, {2719,1,0,3}, {2729,1,0,3}, {2731,1,0,3}, {2741,1,0,2},
{2749,1,0,6}, {2753,1,0,3}, {2767,1,0,3}, {2777,1,0,3}, {2789,1,0,2},
{2791,1,0,6}, {2797,1,0,2}, {2801,1,0,3}, {2803,1,0,2}, {2819,1,0,2},
{2833,1,0,5}, {2837,1,0,2}, {2843,1,0,2}, {2851,1,0,2}, {2857,1,0,11},
{2861,1,0,2}, {2879,1,0,7}, {2887,1,0,5}, {2897,1,0,3}, {2903,1,0,5},
{2909,1,0,2}, {2917,1,0,5}, {2927,1,0,5}, {2939,1,0,2}, {2953,1,0,13},
{2957,1,0,2}, {2963,1,0,2}, {2969,1,0,3}, {2971,1,0,10}, {2999,1,0,17},
{3001,1,0,14}, {3011,1,0,2}, {3019,1,0,2}, {3023,1,0,5}, {3037,1,0,2},
{3041,1,0,3}, {3049,1,0,11}, {3061,1,0,6}, {3067,1,0,2}, {3079,1,0,6},
{3083,1,0,2}, {3089,1,0,3}, {3109,1,0,6}, {3119,1,0,7}, {3121,1,0,7},
{3137,1,0,3}, {3163,1,0,3}, {3167,1,0,5}, {3169,1,0,7}, {3181,1,0,7},
{3187,1,0,2}, {3191,1,0,11}, {3203,1,0,2}, {3209,1,0,3}, {3217,1,0,5},
{3221,1,0,10}, {3229,1,0,6}, {3251,1,0,6}, {3253,1,0,2}, {3257,1,0,3},
{3259,1,0,3}, {3271,1,0,3}, {3299,1,0,2}, {3301,1,0,6}, {3307,1,0,2},
{3313,1,0,10}, {3319,1,0,6}, {3323,1,0,2}, {3329,1,0,3}, {3331,1,0,3},
{3343,1,0,5}, {3347,1,0,2}, {3359,1,0,11}, {3361,1,0,22}, {3371,1,0,2},
{3373,1,0,5}, {3389,1,0,3}, {3391,1,0,3}, {3407,1,0,5}, {3413,1,0,2},
{3433,1,0,5}, {3449,1,0,3}, {3457,1,0,7}, {3461,1,0,2}, {3463,1,0,3},
{3467,1,0,2}, {3469,1,0,2}, {3491,1,0,2}, {3499,1,0,2}, {3511,1,0,7},
{3517,1,0,2}, {3527,1,0,5}, {3529,1,0,17}, {3533,1,0,2}, {3539,1,0,2},
{3541,1,0,7}, {3547,1,0,2}, {3557,1,0,2}, {3559,1,0,3}, {3571,1,0,2},
{3581,1,0,2}, {3583,1,0,3}, {3593,1,0,3}, {3607,1,0,5}, {3613,1,0,2},
{3617,1,0,3}, {3623,1,0,5}, {3631,1,0,15}, {3637,1,0,2}, {3643,1,0,2},
{3659,1,0,2}, {3671,1,0,13}, {3673,1,0,5}, {3677,1,0,2}, {3691,1,0,2},
{3697,1,0,5}, {3701,1,0,2}, {3709,1,0,2}, {3719,1,0,7}, {3727,1,0,3},
{3733,1,0,2}, {3739,1,0,7}, {3761,1,0,3}, {3767,1,0,5}, {3769,1,0,7},
{3779,1,0,2}, {3793,1,0,5}, {3797,1,0,2}, {3803,1,0,2}, {3821,1,0,3},
{3823,1,0,3}, {3833,1,0,3}, {3847,1,0,5}, {3851,1,0,2}, {3853,1,0,2},
{3863,1,0,5}, {3877,1,0,2}, {3881,1,0,13}, {3889,1,0,11}, {3907,1,0,2},
{3911,1,0,13}, {3917,1,0,2}, {3919,1,0,3}, {3923,1,0,2}, {3929,1,0,3},
{3931,1,0,2}, {3943,1,0,3}, {3947,1,0,2}, {3967,1,0,6}, {3989,1,0,2},
{4001,1,0,3}, {4003,1,0,2}, {4007,1,0,5}, {4013,1,0,2}, {4019,1,0,2},
{4021,1,0,2}, {4027,1,0,3}, {4049,1,0,3}, {4051,1,0,10}, {4057,1,0,5},
{4073,1,0,3}, {4079,1,0,11}, {4091,1,0,2}, {4093,1,0,2}, {4099,1,0,2},
{4111,1,0,12}, {4127,1,0,5}, {4129,1,0,13}, {4133,1,0,2}, {4139,1,0,2},
{4153,1,0,5}, {4157,1,0,2}, {4159,1,0,3}, {4177,1,0,5}, {4201,1,0,11},
{4211,1,0,6}, {4217,1,0,3}, {4219,1,0,2}, {4229,1,0,2}, {4231,1,0,3},
{4241,1,0,3}, {4243,1,0,2}, {4253,1,0,2}, {4259,1,0,2}, {4261,1,0,2},
{4271,1,0,7}, {4273,1,0,5}, {4283,1,0,2}, {4289,1,0,3}, {4297,1,0,5},
{4327,1,0,3}, {4337,1,0,3}, {4339,1,0,10}, {4349,1,0,2}, {4357,1,0,2},
{4363,1,0,2}, {4373,1,0,2}, {4391,1,0,14}, {4397,1,0,2}, {4409,1,0,3},
{4421,1,0,3}, {4423,1,0,3}, {4441,1,0,21}, {4447,1,0,3}, {4451,1,0,2},
{4457,1,0,3}, {4463,1,0,5}, {4481,1,0,3}, {4483,1,0,2}, {4493,1,0,2},
{4507,1,0,2}, {4513,1,0,7}, {4517,1,0,2}, {4519,1,0,3}, {4523,1,0,5},
{4547,1,0,2}, {4549,1,0,6}, {4561,1,0,11}, {4567,1,0,3}, {4583,1,0,5},
{4591,1,0,11}, {4597,1,0,5}, {4603,1,0,2}, {4621,1,0,2}, {4637,1,0,2},
{4639,1,0,3}, {4643,1,0,5}, {4649,1,0,3}, {4651,1,0,3}, {4657,1,0,15},
{4663,1,0,3}, {4673,1,0,3}, {4679,1,0,11}, {4691,1,0,2}, {4703,1,0,5},
{4721,1,0,6}, {4723,1,0,2}, {4729,1,0,17}, {4733,1,0,5}, {4751,1,0,19},
{4759,1,0,3}, {4783,1,0,6}, {4787,1,0,2}, {4789,1,0,2}, {4793,1,0,3},
{4799,1,0,7}, {4801,1,0,7}, {4813,1,0,2}, {4817,1,0,3}, {4831,1,0,3},
{4861,1,0,11}, {4871,1,0,11}, {4877,1,0,2}, {4889,1,0,3}, {4903,1,0,3},
{4909,1,0,6}, {4919,1,0,13}, {4931,1,0,6}, {4933,1,0,2}, {4937,1,0,3},
{4943,1,0,7}, {4951,1,0,6}, {4957,1,0,2}, {4967,1,0,5}, {4969,1,0,11},
{4973,1,0,2}, {4987,1,0,2}, {4993,1,0,5}, {4999,1,0,3}, {5003,1,0,2},
{5009,1,0,3}, {5011,1,0,2}, {5021,1,0,3}, {5023,1,0,3}, {5039,1,0,11},
{5051,1,0,2}, {5059,1,0,2}, {5077,1,0,2}, {5081,1,0,3}, {5087,1,0,5},
{5099,1,0,2}, {5101,1,0,6}, {5107,1,0,2}, {5113,1,0,19}, {5119,1,0,3},
{5147,1,0,2}, {5153,1,0,5}, {5167,1,0,6}, {5171,1,0,2}, {5179,1,0,2},
{5189,1,0,2}, {5197,1,0,7}, {5209,1,0,17}, {5227,1,0,2}, {5231,1,0,7},
{5233,1,0,10}, {5237,1,0,3}, {5261,1,0,2}, {5273,1,0,3}, {5279,1,0,7},
{5281,1,0,7}, {5297,1,0,3}, {5303,1,0,5}, {5309,1,0,2}, {5323,1,0,5},
{5333,1,0,2}, {5347,1,0,3}, {5351,1,0,11}, {5381,1,0,3}, {5387,1,0,2},
{5393,1,0,3}, {5399,1,0,7}, {5407,1,0,3}, {5413,1,0,5}, {5417,1,0,3},
{5419,1,0,3}, {5431,1,0,3}, {5437,1,0,5}, {5441,1,0,3}, {5443,1,0,2},
{5449,1,0,7}, {5471,1,0,7}, {5477,1,0,2}, {5479,1,0,3}, {5483,1,0,2},
{5501,1,0,2}, {5503,1,0,3}, {5507,1,0,2}, {5519,1,0,13}, {5521,1,0,11},
{5527,1,0,5}, {5531,1,0,10}, {5557,1,0,2}, {5563,1,0,2}, {5569,1,0,13},
{5573,1,0,2}, {5581,1,0,6}, {5591,1,0,11}, {5623,1,0,5}, {5639,1,0,7},
{5641,1,0,14}, {5647,1,0,3}, {5651,1,0,2}, {5653,1,0,5}, {5657,1,0,3},
{5659,1,0,2}, {5669,1,0,3}, {5683,1,0,2}, {5689,1,0,11}, {5693,1,0,2},
{5701,1,0,2}, {5711,1,0,19}, {5717,1,0,2}, {5737,1,0,5}, {5741,1,0,2},
{5743,1,0,10}, {5749,1,0,2}, {5779,1,0,2}, {5783,1,0,7}, {5791,1,0,6},
{5801,1,0,3}, {5807,1,0,5}, {5813,1,0,2}, {5821,1,0,6}, {5827,1,0,2},
{5839,1,0,6}, {5843,1,0,2}, {5849,1,0,3}, {5851,1,0,2}, {5857,1,0,7},
{5861,1,0,3}, {5867,1,0,5}, {5869,1,0,2}, {5879,1,0,11}, {5881,1,0,31},
{5897,1,0,3}, {5903,1,0,5}, {5923,1,0,2}, {5927,1,0,5}, {5939,1,0,2},
{5953,1,0,7}, {5981,1,0,3}, {5987,1,0,2}, {6007,1,0,3}, {6011,1,0,2},
{6029,1,0,2}, {6037,1,0,5}, {6043,1,0,5}, {6047,1,0,5}, {6053,1,0,2},
{6067,1,0,2}, {6073,1,0,10}, {6079,1,0,17}, {6089,1,0,3}, {6091,1,0,7},
{6101,1,0,2}, {6113,1,0,3}, {6121,1,0,7}, {6131,1,0,2}, {6133,1,0,5},
{6143,1,0,5}, {6151,1,0,3}, {6163,1,0,3}, {6173,1,0,2}, {6197,1,0,2},
{6199,1,0,3}, {6203,1,0,2}, {6211,1,0,2}, {6217,1,0,5}, {6221,1,0,3},
{6229,1,0,2}, {6247,1,0,5}, {6257,1,0,3}, {6263,1,0,5}, {6269,1,0,2},
{6271,1,0,11}, {6277,1,0,2}, {6287,1,0,7}, {6299,1,0,2}, {6301,1,0,10},
{6311,1,0,7}, {6317,1,0,2}, {6323,1,0,2}, {6329,1,0,3}, {6337,1,0,10},
{6343,1,0,3}, {6353,1,0,3}, {6359,1,0,13}, {6361,1,0,19}, {6367,1,0,3},
{6373,1,0,2}, {6379,1,0,2}, {6389,1,0,2}, {6397,1,0,2}, {6421,1,0,6},
{6427,1,0,3}, {6449,1,0,3}, {6451,1,0,3}, {6469,1,0,2}, {6473,1,0,3},
{6481,1,0,7}, {6491,1,0,2}, {6521,1,0,6}, {6529,1,0,7}, {6547,1,0,2},
{6551,1,0,17}, {6553,1,0,10}, {6563,1,0,5}, {6569,1,0,3}, {6571,1,0,3},
{6577,1,0,5}, {6581,1,0,14}, {6599,1,0,13}, {6607,1,0,3}, {6619,1,0,2},
{6637,1,0,2}, {6653,1,0,2}, {6659,1,0,2}, {6661,1,0,6}, {6673,1,0,5},
{6679,1,0,7}, {6689,1,0,3}, {6691,1,0,2}, {6701,1,0,2}, {6703,1,0,5},
{6709,1,0,2}, {6719,1,0,11}, {6733,1,0,2}, {6737,1,0,3}, {6761,1,0,3},
{6763,1,0,2}, {6779,1,0,2}, {6781,1,0,2}, {6791,1,0,7}, {6793,1,0,10},
{6803,1,0,2}, {6823,1,0,3}, {6827,1,0,2}, {6829,1,0,2}, {6833,1,0,3},
{6841,1,0,22}, {6857,1,0,3}, {6863,1,0,5}, {6869,1,0,2}, {6871,1,0,3},
{6883,1,0,2}, {6899,1,0,2}, {6907,1,0,2}, {6911,1,0,7}, {6917,1,0,2},
{6947,1,0,2}, {6949,1,0,2}, {6959,1,0,7}, {6961,1,0,13}, {6967,1,0,5},
{6971,1,0,2}, {6977,1,0,3}, {6983,1,0,5}, {6991,1,0,6}, {6997,1,0,5},
{7001,1,0,3}, {7013,1,0,2}, {7019,1,0,2}, {7027,1,0,2}, {7039,1,0,3},
{7043,1,0,2}, {7057,1,0,5}, {7069,1,0,2}, {7079,1,0,7}, {7103,1,0,5},
{7109,1,0,2}, {7121,1,0,3}, {7127,1,0,5}, {7129,1,0,7}, {7151,1,0,7},
{7159,1,0,3}, {7177,1,0,10}, {7187,1,0,2}, {7193,1,0,3}, {7207,1,0,3},
{7211,1,0,2}, {7213,1,0,5}, {7219,1,0,2}, {7229,1,0,2}, {7237,1,0,2},
{7243,1,0,2}, {7247,1,0,5}, {7253,1,0,2}, {7283,1,0,2}, {7297,1,0,5},
{7307,1,0,2}, {7309,1,0,6}, {7321,1,0,7}, {7331,1,0,2}, {7333,1,0,6},
{7349,1,0,2}, {7351,1,0,6}, {7369,1,0,7}, {7393,1,0,5}, {7411,1,0,2},
{7417,1,0,5}, {7433,1,0,3}, {7451,1,0,2}, {7457,1,0,3}, {7459,1,0,2},
{7477,1,0,2}, {7481,1,0,6}, {7487,1,0,5}, {7489,1,0,7}, {7499,1,0,2},
{7507,1,0,2}, {7517,1,0,2}, {7523,1,0,2}, {7529,1,0,3}, {7537,1,0,7},
{7541,1,0,2}, {7547,1,0,2}, {7549,1,0,2}, {7559,1,0,13}, {7561,1,0,13},
{7573,1,0,2}, {7577,1,0,3}, {7583,1,0,5}, {7589,1,0,2}, {7591,1,0,6},
{7603,1,0,2}, {7607,1,0,5}, {7621,1,0,2}, {7639,1,0,7}, {7643,1,0,2},
{7649,1,0,3}, {7669,1,0,2}, {7673,1,0,3}, {7681,1,0,17}, {7687,1,0,6},
{7691,1,0,2}, {7699,1,0,3}, {7703,1,0,5}, {7717,1,0,2}, {7723,1,0,3},
{7727,1,0,5}, {7741,1,0,7}, {7753,1,0,10}, {7757,1,0,2}, {7759,1,0,3},
{7789,1,0,2}, {7793,1,0,3}, {7817,1,0,3}, {7823,1,0,5}, {7829,1,0,2},
{7841,1,0,12}, {7853,1,0,2}, {7867,1,0,3}, {7873,1,0,5}, {7877,1,0,2},
{7879,1,0,3}, {7883,1,0,2}, {7901,1,0,2}, {7907,1,0,2}, {7919,1,0,7},
{7927,1,0,3}, {7933,1,0,2}, {7937,1,0,3}, {7949,1,0,2}, {7951,1,0,6},
{7963,1,0,5}, {7993,1,0,5}, {8009,1,0,3}, {8011,1,0,14}, {8017,1,0,5},
{8039,1,0,11}, {8053,1,0,2}, {8059,1,0,3}, {8069,1,0,2}, {8081,1,0,3},
{8087,1,0,5}, {8089,1,0,17}, {8093,1,0,2}, {8101,1,0,6}, {8111,1,0,11},
{8117,1,0,2}, {8123,1,0,2}, {8147,1,0,2}, {8161,1,0,7}, {8167,1,0,3},
{8171,1,0,2}, {8179,1,0,2}, {8191,1,0,17}, {8209,1,0,7}, {8219,1,0,2},
{8221,1,0,2}, {8231,1,0,11}, {8233,1,0,10}, {8237,1,0,2}, {8243,1,0,2},
{8263,1,0,3}, {8269,1,0,2}, {8273,1,0,3}, {8287,1,0,3}, {8291,1,0,2},
{8293,1,0,2}, {8297,1,0,3}, {8311,1,0,3}, {8317,1,0,6}, {8329,1,0,7},
{8353,1,0,5}, {8363,1,0,2}, {8369,1,0,3}, {8377,1,0,5}, {8387,1,0,2},
{8389,1,0,6}, {8419,1,0,3}, {8423,1,0,5}, {8429,1,0,2}, {8431,1,0,3},
{8443,1,0,2}, {8447,1,0,5}, {8461,1,0,6}, {8467,1,0,2}, {8501,1,0,7},
{8513,1,0,5}, {8521,1,0,13}, {8527,1,0,5}, {8537,1,0,3}, {8539,1,0,2},
{8543,1,0,5}, {8563,1,0,2}, {8573,1,0,2}, {8581,1,0,6}, {8597,1,0,2},
{8599,1,0,3}, {8609,1,0,3}, {8623,1,0,3}, {8627,1,0,2}, {8629,1,0,6},
{8641,1,0,17}, {8647,1,0,3}, {8663,1,0,5}, {8669,1,0,2}, {8677,1,0,2},
{8681,1,0,15}, {8689,1,0,13}, {8693,1,0,2}, {8699,1,0,2}, {8707,1,0,5},
{8713,1,0,5}, {8719,1,0,3}, {8731,1,0,2}, {8737,1,0,5}, {8741,1,0,2},
{8747,1,0,2}, {8753,1,0,3}, {8761,1,0,23}, {8779,1,0,11}, {8783,1,0,5},
{8803,1,0,2}, {8807,1,0,5}, {8819,1,0,2}, {8821,1,0,2}, {8831,1,0,7},
{8837,1,0,2}, {8839,1,0,3}, {8849,1,0,3}, {8861,1,0,2}, {8863,1,0,3},
{8867,1,0,2}, {8887,1,0,3}, {8893,1,0,5}, {8923,1,0,2}, {8929,1,0,11},
{8933,1,0,2}, {8941,1,0,6}, {8951,1,0,13}, {8963,1,0,2}, {8969,1,0,3},
{8971,1,0,2}, {8999,1,0,7}, {9001,1,0,7}, {9007,1,0,3}, {9011,1,0,2},
{9013,1,0,5}, {9029,1,0,2}, {9041,1,0,3}, {9043,1,0,3}, {9049,1,0,7},
{9059,1,0,2}, {9067,1,0,3}, {9091,1,0,3}, {9103,1,0,6}, {9109,1,0,10},
{9127,1,0,3}, {9133,1,0,6}, {9137,1,0,3}, {9151,1,0,3}, {9157,1,0,6},
{9161,1,0,3}, {9173,1,0,2}, {9181,1,0,2}, {9187,1,0,3}, {9199,1,0,3},
{9203,1,0,2}, {9209,1,0,3}, {9221,1,0,2}, {9227,1,0,2}, {9239,1,0,19},
{9241,1,0,13}, {9257,1,0,3}, {9277,1,0,5}, {9281,1,0,3}, {9283,1,0,2},
{9293,1,0,2}, {9311,1,0,7}, {9319,1,0,3}, {9323,1,0,2}, {9337,1,0,5},
{9341,1,0,2}, {9343,1,0,5}, {9349,1,0,2}, {9371,1,0,2}, {9377,1,0,3},
{9391,1,0,3}, {9397,1,0,2}, {9403,1,0,3}, {9413,1,0,3}, {9419,1,0,2},
{9421,1,0,2}, {9431,1,0,7}, {9433,1,0,5}, {9437,1,0,2}, {9439,1,0,22},
{9461,1,0,3}, {9463,1,0,3}, {9467,1,0,2}, {9473,1,0,3}, {9479,1,0,7},
{9491,1,0,2}, {9497,1,0,3}, {9511,1,0,3}, {9521,1,0,3}, {9533,1,0,2},
{9539,1,0,2}, {9547,1,0,2}, {9551,1,0,11}, {9587,1,0,2}, {9601,1,0,13},
{9613,1,0,2}, {9619,1,0,2}, {9623,1,0,5}, {9629,1,0,2}, {9631,1,0,3},
{9643,1,0,2}, {9649,1,0,7}, {9661,1,0,2}, {9677,1,0,2}, {9679,1,0,3},
{9689,1,0,3}, {9697,1,0,10}, {9719,1,0,17}, {9721,1,0,7}, {9733,1,0,2},
{9739,1,0,3}, {9743,1,0,5}, {9749,1,0,2}, {9767,1,0,5}, {9769,1,0,13},
{9781,1,0,6}, {9787,1,0,3}, {9791,1,0,11}, {9803,1,0,2}, {9811,1,0,3},
{9817,1,0,5}, {9829,1,0,10}, {9833,1,0,3}, {9839,1,0,7}, {9851,1,0,2},
{9857,1,0,5}, {9859,1,0,2}, {9871,1,0,3}, {9883,1,0,2}, {9887,1,0,5},
{9901,1,0,2}, {9907,1,0,2}, {9923,1,0,2}, {9929,1,0,3}, {9931,1,0,10},
{9941,1,0,2}, {9949,1,0,2}, {9967,1,0,3}, {9973,1,0,11}, {10007,1,0,5},
{10009,1,0,11}, {10037,1,0,2}, {10039,1,0,3}, {10061,1,0,3}, {10067,1,0,2},
{10069,1,0,2}, {10079,1,0,11}, {10091,1,0,2}, {10093,1,0,2}, {10099,1,0,2},
{10103,1,0,5}, {10111,1,0,12}, {10133,1,0,2}, {10139,1,0,2}, {10141,1,0,2},
{10151,1,0,7}, {10159,1,0,3}, {10163,1,0,2}, {10169,1,0,3}, {10177,1,0,7},
{10181,1,0,2}, {10193,1,0,3}, {10211,1,0,6}, {10223,1,0,5}, {10243,1,0,7},
{10247,1,0,5}, {10253,1,0,2}, {10259,1,0,2}, {10267,1,0,2}, {10271,1,0,7},
{10273,1,0,10}, {10289,1,0,3}, {10301,1,0,2}, {10303,1,0,3}, {10313,1,0,3},
{10321,1,0,7}, {10331,1,0,2}, {10333,1,0,5}, {10337,1,0,3}, {10343,1,0,5},
{10357,1,0,2}, {10369,1,0,13}, {10391,1,0,19}, {10399,1,0,6}, {10427,1,0,2},
{10429,1,0,7}, {10433,1,0,3}, {10453,1,0,5}, {10457,1,0,3}, {10459,1,0,2},
{10463,1,0,5}, {10477,1,0,2}, {10487,1,0,5}, {10499,1,0,2}, {10501,1,0,2},
{10513,1,0,7}, {10529,1,0,3}, {10531,1,0,3}, {10559,1,0,23}, {10567,1,0,6},
{10589,1,0,2}, {10597,1,0,5}, {10601,1,0,3}, {10607,1,0,5}, {10613,1,0,2},
{10627,1,0,5}, {10631,1,0,11}, {10639,1,0,6}, {10651,1,0,7}, {10657,1,0,7},
{10663,1,0,3}, {10667,1,0,2}, {10687,1,0,5}, {10691,1,0,2}, {10709,1,0,2},
{10711,1,0,3}, {10723,1,0,2}, {10729,1,0,7}, {10733,1,0,2}, {10739,1,0,6},
{10753,1,0,11}, {10771,1,0,3}, {10781,1,0,10}, {10789,1,0,2}, {10799,1,0,19},
{10831,1,0,7}, {10837,1,0,2}, {10847,1,0,5}, {10853,1,0,2}, {10859,1,0,2},
{10861,1,0,2}, {10867,1,0,2}, {10883,1,0,2}, {10889,1,0,3}, {10891,1,0,2},
{10903,1,0,3}, {10909,1,0,2}, {10937,1,0,3}, {10939,1,0,3}, {10949,1,0,2},
{10957,1,0,5}, {10973,1,0,2}, {10979,1,0,2}, {10987,1,0,2}, {10993,1,0,7},
{11003,1,0,2}, {11027,1,0,2}, {11047,1,0,3}, {11057,1,0,3}, {11059,1,0,10},
{11069,1,0,2}, {11071,1,0,3}, {11083,1,0,2}, {11087,1,0,5}, {11093,1,0,2},
{11113,1,0,13}, {11117,1,0,3}, {11119,1,0,3}, {11131,1,0,2}, {11149,1,0,10},
{11159,1,0,7}, {11161,1,0,7}, {11171,1,0,2}, {11173,1,0,5}, {11177,1,0,3},
{11197,1,0,2}, {11213,1,0,2}, {11239,1,0,3}, {11243,1,0,5}, {11251,1,0,13},
{11257,1,0,10}, {11261,1,0,2}, {11273,1,0,3}, {11279,1,0,7}, {11287,1,0,3},
{11299,1,0,3}, {11311,1,0,3}, {11317,1,0,2}, {11321,1,0,3}, {11329,1,0,7},
{11351,1,0,7}, {11353,1,0,7}, {11369,1,0,3}, {11383,1,0,5}, {11393,1,0,3},
{11399,1,0,11}, {11411,1,0,7}, {11423,1,0,5}, {11437,1,0,2}, {11443,1,0,2},
{11447,1,0,5}, {11467,1,0,5}, {11471,1,0,11}, {11483,1,0,2}, {11489,1,0,3},
{11491,1,0,3}, {11497,1,0,7}, {11503,1,0,3}, {11519,1,0,7}, {11527,1,0,5},
{11549,1,0,2}, {11551,1,0,7}, {11579,1,0,2}, {11587,1,0,2}, {11593,1,0,5},
{11597,1,0,3}, {11617,1,0,10}, {11621,1,0,2}, {11633,1,0,3}, {11657,1,0,3},
{11677,1,0,2}, {11681,1,0,3}, {11689,1,0,7}, {11699,1,0,2}, {11701,1,0,6},
{11717,1,0,2}, {11719,1,0,6}, {11731,1,0,3}, {11743,1,0,3}, {11777,1,0,3},
{11779,1,0,2}, {11783,1,0,5}, {11789,1,0,2}, {11801,1,0,3}, {11807,1,0,5},
{11813,1,0,2}, {11821,1,0,2}, {11827,1,0,2}, {11831,1,0,7}, {11833,1,0,5},
{11839,1,0,3}, {11863,1,0,3}, {11867,1,0,2}, {11887,1,0,3}, {11897,1,0,3},
{11903,1,0,5}, {11909,1,0,2}, {11923,1,0,5}, {11927,1,0,5}, {11933,1,0,2},
{11939,1,0,2}, {11941,1,0,10}, {11953,1,0,5}, {11959,1,0,3}, {11969,1,0,3},
{11971,1,0,10}, {11981,1,0,2}, {11987,1,0,2}, {12007,1,0,13}, {12011,1,0,2},
{12037,1,0,5}, {12041,1,0,3}, {12043,1,0,2}, {12049,1,0,13}, {12071,1,0,11},
{12073,1,0,7}, {12097,1,0,5}, {12101,1,0,3}, {12107,1,0,2}, {12109,1,0,6},
{12113,1,0,3}, {12119,1,0,7}, {12143,1,0,10}, {12149,1,0,2}, {12157,1,0,2},
{12161,1,0,3}, {12163,1,0,5}, {12197,1,0,2}, {12203,1,0,2}, {12211,1,0,2},
{12227,1,0,2}, {12239,1,0,13}, {12241,1,0,7}, {12251,1,0,2}, {12253,1,0,2},
{12263,1,0,5}, {12269,1,0,2}, {12277,1,0,2}, {12281,1,0,3}, {12289,1,0,11},
{12301,1,0,2}, {12323,1,0,2}, {12329,1,0,3}, {12343,1,0,7}, {12347,1,0,2},
{12373,1,0,2}, {12377,1,0,6}, {12379,1,0,2}, {12391,1,0,26}, {12401,1,0,3},
{12409,1,0,7}, {12413,1,0,2}, {12421,1,0,7}, {12433,1,0,13}, {12437,1,0,2},
{12451,1,0,3}, {12457,1,0,10}, {12473,1,0,3}, {12479,1,0,23}, {12487,1,0,3},
{12491,1,0,2}, {12497,1,0,3}, {12503,1,0,5}, {12511,1,0,3}, {12517,1,0,6},
{12527,1,0,5}, {12539,1,0,2}, {12541,1,0,14}, {12547,1,0,2}, {12553,1,0,5},
{12569,1,0,3}, {12577,1,0,10}, {12583,1,0,5}, {12589,1,0,2}, {12601,1,0,11},
{12611,1,0,2}, {12613,1,0,2}, {12619,1,0,2}, {12637,1,0,2}, {12641,1,0,3},
{12647,1,0,5}, {12653,1,0,2}, {12659,1,0,2}, {12671,1,0,14}, {12689,1,0,3},
{12697,1,0,7}, {12703,1,0,3}, {12713,1,0,3}, {12721,1,0,13}, {12739,1,0,2},
{12743,1,0,5}, {12757,1,0,2}, {12763,1,0,2}, {12781,1,0,2}, {12791,1,0,7},
{12799,1,0,13}, {12809,1,0,3}, {12821,1,0,2}, {12823,1,0,3}, {12829,1,0,2},
{12841,1,0,21}, {12853,1,0,5}, {12889,1,0,13}, {12893,1,0,3}, {12899,1,0,2},
{12907,1,0,2}, {12911,1,0,23}, {12917,1,0,2}, {12919,1,0,6}, {12923,1,0,2},
{12941,1,0,2}, {12953,1,0,3}, {12959,1,0,7}, {12967,1,0,3}, {12973,1,0,14},
{12979,1,0,2}, {12983,1,0,5}, {13001,1,0,3}, {13003,1,0,5}, {13007,1,0,5},
{13009,1,0,7}, {13033,1,0,5}, {13037,1,0,2}, {13043,1,0,2}, {13049,1,0,3},
{13063,1,0,5}, {13093,1,0,6}, {13099,1,0,3}, {13103,1,0,5}, {13109,1,0,2},
{13121,1,0,7}, {13127,1,0,5}, {13147,1,0,2}, {13151,1,0,13}, {13159,1,0,3},
{13163,1,0,2}, {13171,1,0,11}, {13177,1,0,5}, {13183,1,0,3}, {13187,1,0,2},
{13217,1,0,3}, {13219,1,0,3}, {13229,1,0,2}, {13241,1,0,3}, {13249,1,0,7},
{13259,1,0,6}, {13267,1,0,3}, {13291,1,0,2}, {13297,1,0,5}, {13309,1,0,6},
{13313,1,0,3}, {13327,1,0,3}, {13331,1,0,2}, {13337,1,0,3}, {13339,1,0,2},
{13367,1,0,5}, {13381,1,0,10}, {13397,1,0,2}, {13399,1,0,3}, {13411,1,0,2},
{13417,1,0,5}, {13421,1,0,10}, {13441,1,0,11}, {13451,1,0,2}, {13457,1,0,3},
{13463,1,0,5}, {13469,1,0,2}, {13477,1,0,2}, {13487,1,0,5}, {13499,1,0,6},
{13513,1,0,5}, {13523,1,0,2}, {13537,1,0,7}, {13553,1,0,3}, {13567,1,0,3},
{13577,1,0,3}, {13591,1,0,3}, {13597,1,0,5}, {13613,1,0,2}, {13619,1,0,2},
{13627,1,0,2}, {13633,1,0,5}, {13649,1,0,3}, {13669,1,0,6}, {13679,1,0,7},
{13681,1,0,22}, {13687,1,0,3}, {13691,1,0,2}, {13693,1,0,6}, {13697,1,0,3},
{13709,1,0,2}, {13711,1,0,6}, {13721,1,0,3}, {13723,1,0,2}, {13729,1,0,23},
{13751,1,0,11}, {13757,1,0,2}, {13759,1,0,6}, {13763,1,0,2}, {13781,1,0,7},
{13789,1,0,7}, {13799,1,0,7}, {13807,1,0,5}, {13829,1,0,2}, {13831,1,0,6},
{13841,1,0,6}, {13859,1,0,2}, {13873,1,0,5}, {13877,1,0,2}, {13879,1,0,6},
{13883,1,0,2}, {13901,1,0,2}, {13903,1,0,3}, {13907,1,0,2}, {13913,1,0,3},
{13921,1,0,7}, {13931,1,0,2}, {13933,1,0,2}, {13963,1,0,3}, {13967,1,0,5},
{13997,1,0,2}, {13999,1,0,3}, {14009,1,0,3}, {14011,1,0,2}, {14029,1,0,6},
{14033,1,0,3}, {14051,1,0,2}, {14057,1,0,3}, {14071,1,0,7}, {14081,1,0,3},
{14083,1,0,3}, {14087,1,0,5}, {14107,1,0,2}, {14143,1,0,3}, {14149,1,0,6},
{14153,1,0,3}, {14159,1,0,13}, {14173,1,0,2}, {14177,1,0,3}, {14197,1,0,11},
{14207,1,0,5}, {14221,1,0,2}, {14243,1,0,2}, {14249,1,0,3}, {14251,1,0,3},
{14281,1,0,19}, {14293,1,0,6}, {14303,1,0,5}, {14321,1,0,3}, {14323,1,0,5},
{14327,1,0,5}, {14341,1,0,2}, {14347,1,0,3}, {14369,1,0,3}, {14387,1,0,2},
{14389,1,0,2}, {14401,1,0,11}, {14407,1,0,19}, {14411,1,0,2}, {14419,1,0,2},
{14423,1,0,5}, {14431,1,0,3}, {14437,1,0,5}, {14447,1,0,5}, {14449,1,0,22},
{14461,1,0,2}, {14479,1,0,3}, {14489,1,0,3}, {14503,1,0,3}, {14519,1,0,13},
{14533,1,0,2}, {14537,1,0,3}, {14543,1,0,5}, {14549,1,0,2}, {14551,1,0,3},
{14557,1,0,2}, {14561,1,0,6}, {14563,1,0,3}, {14591,1,0,11}, {14593,1,0,5},
{14621,1,0,2}, {14627,1,0,2}, {14629,1,0,2}, {14633,1,0,3}, {14639,1,0,11},
{14653,1,0,2}, {14657,1,0,3}, {14669,1,0,2}, {14683,1,0,3}, {14699,1,0,2},
{14713,1,0,5}, {14717,1,0,2}, {14723,1,0,2}, {14731,1,0,10}, {14737,1,0,10},
{14741,1,0,2}, {14747,1,0,2}, {14753,1,0,3}, {14759,1,0,17}, {14767,1,0,3},
{14771,1,0,2}, {14779,1,0,3}, {14783,1,0,5}, {14797,1,0,2}, {14813,1,0,2},
{14821,1,0,2}, {14827,1,0,2}, {14831,1,0,11}, {14843,1,0,2}, {14851,1,0,2},
{14867,1,0,2}, {14869,1,0,2}, {14879,1,0,7}, {14887,1,0,3}, {14891,1,0,2},
{14897,1,0,3}, {14923,1,0,2}, {14929,1,0,7}, {14939,1,0,2}, {14947,1,0,2},
{14951,1,0,19}, {14957,1,0,2}, {14969,1,0,3}, {14983,1,0,3}, {15013,1,0,2},
{15017,1,0,3}, {15031,1,0,3}, {15053,1,0,2}, {15061,1,0,2}, {15073,1,0,5},
{15077,1,0,2}, {15083,1,0,2}, {15091,1,0,2}, {15101,1,0,2}, {15107,1,0,2},
{15121,1,0,11}, {15131,1,0,2}, {15137,1,0,3}, {15139,1,0,2}, {15149,1,0,2},
{15161,1,0,3}, {15173,1,0,2}, {15187,1,0,2}, {15193,1,0,5}, {15199,1,0,6},
{15217,1,0,10}, {15227,1,0,2}, {15233,1,0,3}, {15241,1,0,11}, {15259,1,0,2},
{15263,1,0,5}, {15269,1,0,2}, {15271,1,0,11}, {15277,1,0,6}, {15287,1,0,5},
{15289,1,0,11}, {15299,1,0,2}, {15307,1,0,3}, {15313,1,0,5}, {15319,1,0,3},
{15329,1,0,3}, {15331,1,0,2}, {15349,1,0,2}, {15359,1,0,11}, {15361,1,0,7},
{15373,1,0,2}, {15377,1,0,3}, {15383,1,0,5}, {15391,1,0,12}, {15401,1,0,6},
{15413,1,0,2}, {15427,1,0,2}, {15439,1,0,3}, {15443,1,0,2}, {15451,1,0,3},
{15461,1,0,2}, {15467,1,0,5}, {15473,1,0,3}, {15493,1,0,5}, {15497,1,0,3},
{15511,1,0,3}, {15527,1,0,5}, {15541,1,0,6}, {15551,1,0,7}, {15559,1,0,3},
{15569,1,0,3}, {15581,1,0,2}, {15583,1,0,5}, {15601,1,0,23}, {15607,1,0,3},
{15619,1,0,7}, {15629,1,0,2}, {15641,1,0,3}, {15643,1,0,5}, {15647,1,0,5},
{15649,1,0,11}, {15661,1,0,2}, {15667,1,0,2}, {15671,1,0,13}, {15679,1,0,11},
{15683,1,0,2}, {15727,1,0,3}, {15731,1,0,2}, {15733,1,0,6}, {15737,1,0,3},
{15739,1,0,2}, {15749,1,0,2}, {15761,1,0,3}, {15767,1,0,5}, {15773,1,0,2},
{15787,1,0,2}, {15791,1,0,29}, {15797,1,0,2}, {15803,1,0,2}, {15809,1,0,3},
{15817,1,0,5}, {15823,1,0,3}, {15859,1,0,2}, {15877,1,0,5}, {15881,1,0,3},
{15887,1,0,5}, {15889,1,0,21}, {15901,1,0,10}, {15907,1,0,2}, {15913,1,0,5},
{15919,1,0,6}, {15923,1,0,2}, {15937,1,0,7}, {15959,1,0,11}, {15971,1,0,2},
{15973,1,0,7}, {15991,1,0,12}, {16001,1,0,3}, {16007,1,0,5}, {16033,1,0,5},
{16057,1,0,7}, {16061,1,0,12}, {16063,1,0,5}, {16067,1,0,2}, {16069,1,0,2},
{16073,1,0,3}, {16087,1,0,5}, {16091,1,0,6}, {16097,1,0,3}, {16103,1,0,5},
{16111,1,0,7}, {16127,1,0,5}, {16139,1,0,2}, {16141,1,0,6}, {16183,1,0,3},
{16187,1,0,2}, {16189,1,0,2}, {16193,1,0,5}, {16217,1,0,3}, {16223,1,0,5},
{16229,1,0,2}, {16231,1,0,3}, {16249,1,0,17}, {16253,1,0,2}, {16267,1,0,3},
{16273,1,0,7}, {16301,1,0,2}, {16319,1,0,7}, {16333,1,0,2}, {16339,1,0,2},
{16349,1,0,2}, {16361,1,0,3}, {16363,1,0,2}, {16369,1,0,7}, {16381,1,0,2},
};

void dec_um(int p,int a,UM u)
{
  int i;

  for ( i = 0; a; i++, a /= p )
    COEF(u)[i] = a%p;
  DEG(u) = i-1;
}

/*
 * an element of GF(p^n) f(x)=a(n-1)*x^(n-1)+...+a(0)
 * is encodeded to f(p).
 * current_gfs_iton[i] = r^i mod p (i=0,...,p-2)
 * current_gfs_iton[p-1] = 0
 */

void setmod_sf(int p,int n)
{
  int r,i,q1,q,t,t1;
  UM dp;

  if ( p >= SF_THRESHOLD ) {
    if ( n > 1 )
      error("setmod_ff : p^n is too large");
    current_gfs_p = p;
    current_gfs_q = p;
    current_gfs_q1 = p-1;
    current_gfs_ext = 0;
    current_gfs_ntoi = 0;
    current_gfs_iton = 0;
    current_gfs_plus1 = 0;
    return;
  }

  for ( i = 0, q = 1; i < n; i++ )
    q *= p;
    if ( p == current_gfs_p && q == current_gfs_q ) return;
  dp = UMALLOC(n);
  r = search_defpoly_and_primitive_root(p,n,dp);
  if ( !r ) {
    generate_defpoly_um(p,n,dp);
    r = generate_primitive_root_enc(p,n,dp);
    if ( !r )
      error("setmod_sf : primitive root not found");
  }
  current_gfs_p = p;
  current_gfs_q = q;
  current_gfs_q1 = q1 = q-1;
  if ( n > 1 )
    umtop(CO->v,dp,&current_gfs_ext);
  else
    current_gfs_ext = 0;
  current_gfs_iton = (int *)MALLOC(q1*sizeof(int));
  current_gfs_iton[0] = 1;
  for ( i = 1; i < q1; i++ )
    current_gfs_iton[i] = mulremum_enc(p,n,dp,current_gfs_iton[i-1],r);

  current_gfs_ntoi = (int *)MALLOC(q*sizeof(int));
  current_gfs_ntoi[0] = -1;
  for ( i = 0; i < q1; i++ )
    current_gfs_ntoi[current_gfs_iton[i]] = i;
    
  current_gfs_plus1 = (int *)MALLOC(q*sizeof(int));
  for ( i = 0; i < q1; i++ ) {
    t = current_gfs_iton[i];
    /* add 1 to the constant part */
    t1 = (t/p)*p+((t+1)%p);
    current_gfs_plus1[i] = current_gfs_ntoi[t1];
  }
}

int search_defpoly_and_primitive_root(int p,int n,UM dp)
{
  int l,min,max,mid,p1,i,ind,t;

  l = sizeof(prim_root_info_tab)/sizeof(struct prim_root_info);
  min = 0; max = l-1;
  ind = -1;
  while ( max - min > 1 ) {
    mid = (max+min)/2;
    p1 = prim_root_info_tab[mid].p;
    if ( p1 == p ) {
      ind = mid; break;
    } else if ( p1 > p )
      max = mid;
    else
      min = mid;
  }
  if ( ind < 0 ) {
    if ( prim_root_info_tab[min].p == p )
      ind = min;
    else if ( prim_root_info_tab[max].p == p )
      ind = max;
    else
      return 0; /* XXX */
  }
  /* now prim_root_info_tab[ind].p = p */
  t = ind - (prim_root_info_tab[ind].extdeg-1);
  /* now prim_root_info_tab[t].extdeg = 1 */
  for ( i = t; prim_root_info_tab[i].p == p; i++ )
    if ( prim_root_info_tab[i].extdeg == n )
      break;
  if ( prim_root_info_tab[i].p != p )
    return 0;
  dec_um(p,prim_root_info_tab[i].defpoly,dp);
  return prim_root_info_tab[i].prim_root;
}

void generate_defpoly_um(int p,int n,UM dp)
{
  int i,j,a,q;
  UM wf,wdf,wgcd;

  wf = W_UMALLOC(n);
  wdf = W_UMALLOC(n);
  wgcd = W_UMALLOC(n);
  COEF(dp)[n] = 1;
  DEG(dp) = n;
  for ( i = 0, q = 1; i < n; i++ )
    q *= p;
  for ( i = 0; i < q; i++ ) {
    for ( j = 0, a = i; a; j++, a /= p )
      COEF(dp)[j] = a%p;
    for ( ; j < n; j++ )
      COEF(dp)[j] = 0;
    cpyum(dp,wf);
    diffum(p,dp,wdf);
    gcdum(p,wf,wdf,wgcd);
    if ( DEG(wgcd) >= 1 )
      continue;
    mini(p,dp,wf);
    if ( DEG(wf) <= 0 )
      return;
  }
}

int generate_primitive_root_enc(int p,int n,UM dp)
{
  int i,r,rj,j,q;

  if ( p == 2 && n == 1 )
    return 1;

  for ( i = 0, q = 1; i < n; i++ )
     q *= p;
  for ( r = n==1?2:p; r < q; r++ ) {
    rj = r;
    for ( j = 1; j < q-1 && rj != 1; j++ )
      rj = mulremum_enc(p,n,dp,rj,r);
    if ( j == q-1 )
      return r;
  }
  /* not found */
  return 0;
}

/* [a(p)]*[b(p)] in GF(p^n) -> [a(x)*b(x) mod dp(x)]_{x->p} */

int mulremum_enc(int p,int n,UM dp,int a,int b)
{
  int i,dr,r;
  UM wa,wb,wc,wq;

  if ( n == 1 )
    return (a*b)%p;
  if ( !a || !b )
    return 0;

  wa = W_UMALLOC(n);
  dec_um(p,a,wa);

  wb = W_UMALLOC(n);
  dec_um(p,b,wb);

  wc = W_UMALLOC(2*n);
  wq = W_UMALLOC(2*n);
  mulum(p,wa,wb,wc);
  dr = divum(p,wc,dp,wq);
  for ( i = dr, r = 0; i >= 0; i-- )
    r = r*p+COEF(wc)[i];
  return r;
}

/* sigma : alpha -> alpha^q */

void gfs_galois_action(GFS a,Q e,GFS *c)
{
  Z p;
  int i,k;
  GFS t,s;

  t = a;
  k = ZTOS(e);
  STOZ(current_gfs_p,p);
  for ( i = 0; i < k; i++ ) {
    pwrgfs(t,p,&s); t = s;
  }
  *c = t;
}

/* GF(pn)={0,1,a,a^2,...} -> GF(pm)={0,1,b,b^2,...}; a->b^k */

void gfs_embed(GFS z,int k,int pm,GFS *c)
{
  int t;

  if ( !z )
    *c = 0;
  else {
    t = dmar(k,CONT(z),0,pm-1);
    MKGFS(t,*c);
  }
}

/* 0 <= index <= q-1 */

void indextogfs(int index, GFS *c)
{
  if ( index == 0 )
    *c = 0;
  else if ( index >= current_gfs_q )
    error("indextogfs : exhausted");
  else if ( !current_gfs_ntoi ) {
    MKGFS(index,*c);
  } else {
    MKGFS(index-1,*c);
  }
}

void itogfs(int n, GFS *c)
{
  n = _itosf(n);
  if ( !n )
    *c = 0;
  else {
    n = IFTOF(n);
    MKGFS(n,*c);
  }
}

void iftogfs(int n, GFS *c)
{
  if ( !n )
    *c = 0;
  else {
    MKGFS(IFTOF(n),*c);
  }
}

void qtogfs(Q a,GFS *c)
{
  int s;

  if ( a && (sgnq(a) < 1) )
    error("qtogfs : invalid argument");
  s = ZTOS(a)%current_gfs_q;
  itogfs(s,c);
}

void mqtogfs(MQ a,GFS *c)
{
  if ( !a )
    *c = 0;
  else
    itogfs(CONT(a),c);
}

void gfstomq(GFS a,MQ *c)
{
  if ( !a )
    *c = 0;
  else if ( !current_gfs_ntoi ) {
    UTOMQ(CONT(a),*c);
  } else {
    UTOMQ(current_gfs_iton[CONT(a)],*c);
  }
}

void gfstopgfs(GFS a,V v,P *c)
{
  MQ t;
  Z q;

  if ( !a )
    *c = 0;
  else if ( !current_gfs_ntoi ) {
    UTOMQ(CONT(a),t);
    STOZ(CONT(t),q);
    *c = (P)q;
  } else
    enc_to_p(current_gfs_p,current_gfs_iton[CONT(a)],v,c);
}

void ntogfs(Obj a,GFS *b)
{
  P t;

  if ( !current_gfs_q1 )
    error("addgfs : current_gfs_q is not set");
  if ( !a || (OID(a)==O_N && NID(a) == N_GFS) )
    *b = (GFS)a;
  else if ( OID(a) == O_N && NID(a) == N_M )
    mqtogfs((MQ)a,b);
  else if ( OID(a) == O_N && NID(a) == N_Q ) {
    ptomp(current_gfs_p,(P)a,&t); mqtogfs((MQ)t,b);
  } else
    error("ntogfs : invalid argument");
}

void addgfs(GFS a,GFS b,GFS *c)
{
  int ai,bi,ci;
  GFS z;

  ntogfs((Obj)a,&z); a = z;
  ntogfs((Obj)b,&z); b = z;
  if ( !a )
    *c = b;
  else if ( !b )
    *c = a;
  else if ( !current_gfs_ntoi ) {
    ai = CONT(a); bi = CONT(b);
    ci = ai+bi-current_gfs_q;
    if ( ci == 0 )
      *c = 0;
    else {
      if ( ci < 0 )
        ci += current_gfs_q;  
      MKGFS(ci,*c);
    }
  } else {
    ai = CONT(a); bi = CONT(b);
    if ( ai > bi ) {
      /* tab[ai]+tab[bi] = tab[bi](tab[ai-bi]+1) */
      ci = current_gfs_plus1[ai-bi];
      if ( ci < 0 )
        *c = 0;
      else {
        ci += bi;
        if ( ci >= current_gfs_q1 )
          ci -= current_gfs_q1;
        MKGFS(ci,*c);
      }
    } else {
      /* tab[ai]+tab[bi] = tab[ai](tab[bi-ai]+1) */
      ci = current_gfs_plus1[bi-ai];
      if ( ci < 0 )
        *c = 0;
      else {
        ci += ai;
        if ( ci >= current_gfs_q1 )
          ci -= current_gfs_q1;
        MKGFS(ci,*c);
      }
    }
  }
}

void subgfs(GFS a,GFS b,GFS *c)
{
  GFS t,z;

  ntogfs((Obj)a,&z); a = z;
  ntogfs((Obj)b,&z); b = z;
  if ( !b )
    *c = a;
  else {
    chsgngfs(b,&t);
    addgfs(a,t,c);
  }
}

void mulgfs(GFS a,GFS b,GFS *c)
{
  int ai,bi,ci;
  GFS z;

  ntogfs((Obj)a,&z); a = z;
  ntogfs((Obj)b,&z); b = z;
  if ( !a || !b )
    *c = 0;
  else if ( !current_gfs_ntoi ) {
    ai = CONT(a); bi = CONT(b);
    DMAR(ai,bi,0,current_gfs_q,ci);
    MKGFS(ci,*c);
  } else {
    ai = CONT(a) + CONT(b);
    if ( ai >= current_gfs_q1 )
      ai -= current_gfs_q1;
    MKGFS(ai,*c);
  }
}

void divgfs(GFS a,GFS b,GFS *c)
{
  int ai,bi,ci;
  GFS z;

  ntogfs((Obj)a,&z); a = z;
  ntogfs((Obj)b,&z); b = z;
  if ( !b )
    error("divgfs : division by 0");
  else if ( !a )
    *c = 0;
  else if ( !current_gfs_ntoi ) {
    ai = CONT(a); bi = invm(CONT(b),current_gfs_q);
    DMAR(ai,bi,0,current_gfs_q,ci);
    MKGFS(ci,*c);
  } else {
    ai = CONT(a) - CONT(b);
    if ( ai < 0 )
      ai += current_gfs_q1;
    MKGFS(ai,*c);
  }
}

void chsgngfs(GFS a,GFS *c)
{
  int ai;
  GFS z;

  ntogfs((Obj)a,&z); a = z;
  if ( !a )
    *c = 0;
  else if ( !current_gfs_ntoi ) {
    ai = current_gfs_q - CONT(a);
    MKGFS(ai,*c);
  } else if ( current_gfs_q1&1 )
    *c = a;
  else {  
    /* r^((q-1)/2) = -1 */
    ai = CONT(a)+(current_gfs_q1>>1);
    if ( ai >= current_gfs_q1 )
      ai -= current_gfs_q1;
    MKGFS(ai,*c);
  }
}

void pwrgfs(GFS a,Z b,GFS *c)
{
  Z an,tn,rn;
  GFS t,s,z;
  int ai;

  ntogfs((Obj)a,&z); a = z;
  if ( !b )
    itogfs(1,c);
  else if ( !a )
    *c = 0;
  else if ( !current_gfs_ntoi) {
    ai = pwrm(current_gfs_q,CONT(a),ZTOS(b));
    MKGFS(ai,*c);
  } else {
    STOZ(CONT(a),an); mulz(an,b,&tn);
    STOZ(current_gfs_q1,an); remz(tn,an,&rn);
    if ( !rn )
      itogfs(1,c);
    else {
      ai = ZTOS(rn);
      MKGFS(ai,*c);
    }
  }
}

int cmpgfs(GFS a,GFS b)
{
  GFS z;

  ntogfs((Obj)a,&z); a = z;
  if ( !a )
    return !b ? 0 : -1;
  else
    if ( !b )
      return 1;
    else {
      if ( CONT(a) > CONT(b) )
        return 1;
      else if ( CONT(a) < CONT(b) )
        return -1;
      else
        return 0;
    }
}

void pthrootgfs(GFS a,GFS *b)
{
  Z p;
  int e,i;
  GFS t,s;

  STOZ(characteristic_sf(),p);
  e = extdeg_sf()-1;
  t = a;
  for ( i = 0; i < e; i++ ) {
    pwrgfs(t,p,&s); t = s;
  }
  *b = t;
}

void randomgfs(GFS *r)
{
  unsigned int t;

  if ( !current_gfs_q1 )
    error("addgfs : current_gfs_q is not set");
  t = mt_genrand()%current_gfs_q;
  indextogfs(t,r);
}

/* arithmetic operations for 'immediate values of GFS */

int _addsf(int a,int b)
{
  if ( !a )
    return b;
  else if ( !b )
    return a;

  a = IFTOF(a); b = IFTOF(b);

  if ( !current_gfs_ntoi ) {
    a = a+b-current_gfs_q;
    if ( a == 0 )
      return 0;
    else { 
      if ( a < 0 )
        a += current_gfs_q;  
      return FTOIF(a);
    }
  }

  if ( a > b ) {
    /* tab[a]+tab[b] = tab[b](tab[a-b]+1) */
    a = current_gfs_plus1[a-b];
    if ( a < 0 )
      return 0;
    else {
      a += b;
      if ( a >= current_gfs_q1 )
        a -= current_gfs_q1;
      return FTOIF(a);
    }
  } else {
    /* tab[a]+tab[b] = tab[a](tab[b-a]+1) */
    b = current_gfs_plus1[b-a];
    if ( b < 0 )
      return 0;
    else {
      b += a;
      if ( b >= current_gfs_q1 )
        b -= current_gfs_q1;
      return FTOIF(b);
    }
  }
}

int _chsgnsf(int a)
{
  if ( !a )
    return 0;
  else if ( !current_gfs_ntoi ) {
    a = current_gfs_q-IFTOF(a);
    return FTOIF(a);
  } else if ( current_gfs_q1&1 )
    return a;
  else {  
    /* r^((q-1)/2) = -1 */
    a = IFTOF(a);
    a += (current_gfs_q1>>1);
    if ( a >= current_gfs_q1 )
      a -= current_gfs_q1;
    return FTOIF(a);
  }
}

int _subsf(int a,int b)
{
  if ( !a )
    return _chsgnsf(b);
  else if ( !b )
    return a;
  else
    return _addsf(a,_chsgnsf(b));
}

int _mulsf(int a,int b)
{
  int c;

  if ( !a || !b )
    return 0;
  else if ( !current_gfs_ntoi ) {
    a = IFTOF(a); b = IFTOF(b);
    DMAR(a,b,0,current_gfs_q,c);
    return FTOIF(c);
  } else {
    a = IFTOF(a) + IFTOF(b);
    if ( a >= current_gfs_q1 )
      a -= current_gfs_q1;
    return FTOIF(a);
  }
}

int _invsf(int a)
{
  if ( !a ) {
    error("_invsf : division by 0");
    /* NOTREACHED */
    return -1;
  } else if ( !current_gfs_ntoi ) {
    a = invm(IFTOF(a),current_gfs_q);
    return FTOIF(a);
  } else {
    a = current_gfs_q1 - IFTOF(a);
    return FTOIF(a);
  }
}

int _divsf(int a,int b)
{
  int c;

  if ( !b ) {
    error("_divsf : division by 0");
    /* NOTREACHED */
    return -1;
  } else if ( !current_gfs_ntoi ) {
    b = invm(IFTOF(b),current_gfs_q);
    a = IFTOF(a);
    DMAR(a,b,0,current_gfs_q,c);
    return FTOIF(c);
  } else if ( !a )
    return 0;
  else {
    a = IFTOF(a) - IFTOF(b);
    if ( a < 0 )
      a += current_gfs_q1;
    return FTOIF(a);
  }
}

int _pwrsf(int a,int b)
{
  GFS at,ct;
  Z bt;
  int c;

  if ( !b )
    return _onesf();
  else if ( !a )
    return 0;
  if ( !current_gfs_ntoi ) {
    a = pwrm(current_gfs_q,IFTOF(a),b);
    return FTOIF(a);
  } else {
    iftogfs(a,&at);
    STOZ(b,bt);
    pwrgfs(at,bt,&ct);
    c = CONT(ct);
    return FTOIF(c);
  }
}

int _onesf()
{
  return !current_gfs_ntoi ? FTOIF(1) : FTOIF(0);
}

int _itosf(int n)
{
  int i;

  /* XXX */
#if 0
  n %= current_gfs_p;
#else
  n %= current_gfs_q;
#endif
  if ( !n )
    return 0;
  i = !current_gfs_ntoi ? n : current_gfs_ntoi[n];
  i = FTOIF(i);
  if ( n < 0 )
    i = _chsgnsf(i);
  return i;
}

int _isonesf(int a)
{
  return a == _onesf();
}

int _randomsf()
{
  int t;

  t = (int) (mt_genrand() % current_gfs_q);
  if ( !current_gfs_ntoi )
    return t ? FTOIF(t) : 0;
  else
    return t!=current_gfs_q1 ? FTOIF(t) : 0;
}

int field_order_sf()
{
  return current_gfs_q;
}

int characteristic_sf()
{
  return current_gfs_p;
}

int extdeg_sf()
{
  if ( !current_gfs_ext )
    return 1;
  else
    return UDEG(current_gfs_ext);
}