Annotation of OpenXM_contrib2/asir2000/engine/M.c, Revision 1.7
1.2 noro 1: /*
2: * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
3: * All rights reserved.
4: *
5: * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
6: * non-exclusive and royalty-free license to use, copy, modify and
7: * redistribute, solely for non-commercial and non-profit purposes, the
8: * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
9: * conditions of this Agreement. For the avoidance of doubt, you acquire
10: * only a limited right to use the SOFTWARE hereunder, and FLL or any
11: * third party developer retains all rights, including but not limited to
12: * copyrights, in and to the SOFTWARE.
13: *
14: * (1) FLL does not grant you a license in any way for commercial
15: * purposes. You may use the SOFTWARE only for non-commercial and
16: * non-profit purposes only, such as academic, research and internal
17: * business use.
18: * (2) The SOFTWARE is protected by the Copyright Law of Japan and
19: * international copyright treaties. If you make copies of the SOFTWARE,
20: * with or without modification, as permitted hereunder, you shall affix
21: * to all such copies of the SOFTWARE the above copyright notice.
22: * (3) An explicit reference to this SOFTWARE and its copyright owner
23: * shall be made on your publication or presentation in any form of the
24: * results obtained by use of the SOFTWARE.
25: * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
1.3 noro 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.2 noro 27: * for such modification or the source code of the modified part of the
28: * SOFTWARE.
29: *
30: * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
31: * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
32: * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
33: * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
34: * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
35: * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
36: * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
37: * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
38: * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
39: * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
40: * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
41: * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
42: * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
43: * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
44: * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
45: * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
46: * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
47: *
1.7 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/engine/M.c,v 1.6 2001/06/25 01:35:21 noro Exp $
1.2 noro 49: */
1.1 noro 50: #include "ca.h"
51: #include "base.h"
52:
53: void addum(mod,p1,p2,pr)
54: int mod;
55: UM p1,p2,pr;
56: {
57: register int *c1,*c2,*cr,i,dmax,dmin;
58:
59: if ( DEG(p1) == -1 ) {
60: cpyum(p2,pr);
61: return;
62: }
63: if ( DEG(p2) == -1 ) {
64: cpyum(p1,pr);
65: return;
66: }
67: if ( DEG(p1) >= DEG(p2) ) {
68: c1 = COEF(p1); c2 = COEF(p2); dmax = DEG(p1); dmin = DEG(p2);
69: } else {
70: c1 = COEF(p2); c2 = COEF(p1); dmax = DEG(p2); dmin = DEG(p1);
71: }
72: for ( i = 0, cr = COEF(pr); i <= dmin; i++ )
73: cr[i] = ( c1[i] + c2[i] ) % mod;
74: for ( ; i <= dmax; i++ )
75: cr[i] = c1[i];
76: if ( dmax == dmin )
77: degum(pr,dmax);
78: else
79: DEG(pr) = dmax;
80: }
81:
82: void subum(mod,p1,p2,pr)
83: int mod;
84: UM p1,p2,pr;
85: {
86: register int *c1,*c2,*cr,i;
87: int dmax,dmin;
88:
89: if ( DEG(p1) == -1 ) {
90: for ( i = DEG(pr) = DEG(p2), c2 = COEF(p2), cr = COEF(pr);
91: i >= 0; i-- )
92: cr[i] = ( mod - c2[i] ) % mod;
93: return;
94: }
95: if ( DEG(p2) == -1 ) {
96: cpyum(p1,pr);
97: return;
98: }
99: c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr);
100: if ( DEG(p1) >= DEG(p2) ) {
101: dmax = DEG(p1); dmin = DEG(p2);
102: for ( i = 0; i <= dmin; i++ )
103: cr[i] = ( c1[i] + mod - c2[i] ) % mod;
104: for ( ; i <= dmax; i++ )
105: cr[i] = c1[i];
106: } else {
107: dmax = DEG(p2); dmin = DEG(p1);
108: for ( i = 0; i <= dmin; i++ )
109: cr[i] = ( c1[i] + mod - c2[i] ) % mod;
110: for ( ; i <= dmax; i++ )
111: cr[i] = ( mod - c2[i] ) % mod;
112: }
113: if ( dmax == dmin )
114: degum(pr,dmax);
115: else
116: DEG(pr) = dmax;
117: }
118:
119: void pwrum(mod,p,e,pr)
120: int mod,e;
121: UM p,pr;
122: {
123: UM wt,ws;
124:
125: if ( e == 0 ) {
126: DEG(pr) = 0; COEF(pr)[0] = 1;
127: } else if ( DEG(p) < 0 )
128: DEG(pr) = -1;
129: else if ( e == 1 )
130: cpyum(p,pr);
131: else if ( DEG(p) == 0 ) {
132: DEG(pr) = 0; COEF(pr)[0] = pwrm(mod,COEF(p)[0],e);
133: } else {
134: wt = W_UMALLOC(DEG(p)*e); ws = W_UMALLOC(DEG(p)*e);
135: pwrum(mod,p,e/2,wt);
136: if ( !(e%2) )
137: mulum(mod,wt,wt,pr);
138: else {
139: mulum(mod,wt,wt,ws); mulum(mod,ws,p,pr);
140: }
141: }
142: }
143:
144: void gcdum(mod,p1,p2,pr)
145: register int mod;
146: UM p1,p2,pr;
147: {
148: register int inv;
149: UM t1,t2,q,tum;
150: int drem;
151:
152: if ( DEG(p1) < 0 )
153: cpyum(p2,pr);
154: else if ( DEG(p2) < 0 )
155: cpyum(p1,pr);
156: else {
157: if ( DEG(p1) >= DEG(p2) ) {
158: t1 = p1; t2 = p2;
159: } else {
160: t1 = p2; t2 = p1;
161: }
162: q = W_UMALLOC(DEG(t1));
163: while ( ( drem = divum(mod,t1,t2,q) ) >= 0 ) {
164: tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem;
165: }
166: inv = invm(COEF(t2)[DEG(t2)],mod);
167: mulsum(mod,t2,inv,pr);
168: }
169: }
170:
171: void eucum(mod,f1,f2,a,b)
172: register int mod;
173: UM f1,f2,a,b;
174: {
175: UM g1,g2,a1,a2,a3,wm,q,tum;
176: int d,dr;
177:
178: d = DEG(f1) + DEG(f2) + 10;
179: g1 = W_UMALLOC(d); g2 = W_UMALLOC(d); a1 = W_UMALLOC(d);
180: a2 = W_UMALLOC(d); a3 = W_UMALLOC(d); wm = W_UMALLOC(d);
181: q = W_UMALLOC(d);
182: DEG(a1) = 0; COEF(a1)[0] = 1; DEG(a2) = -1;
183: cpyum(f1,g1); cpyum(f2,g2);
184: while ( 1 ) {
185: dr = divum(mod,g1,g2,q); tum = g1; g1 = g2; g2 = tum;
186: if ( ( DEG(g2) = dr ) == -1 )
187: break;
188: mulum(mod,a2,q,wm); subum(mod,a1,wm,a3); dr = divum(mod,a3,f2,q);
189: tum = a1; a1 = a2; a2 = a3; a3 = tum; DEG(a3) = dr;
190: }
191: if ( COEF(g1)[0] != 1 )
192: mulsum(mod,a2,invm(COEF(g1)[0],mod),a);
193: else
194: cpyum(a2,a);
195: mulum(mod,a,f1,wm);
196: if ( DEG(wm) >= 0 )
197: COEF(wm)[0] = ( COEF(wm)[0] + mod - 1 ) % mod;
198: else {
199: DEG(wm) = 0; COEF(wm)[0] = mod - 1;
200: }
201: divum(mod,wm,f2,q); mulsum(mod,q,mod-1,b);
202: }
203:
204: void sqfrum(index,count,f,nindex,dcr,pl)
205: int index,count,*nindex;
206: P f;
207: struct oDUM **dcr;
208: ML *pl;
209: {
210: int i,j,m,n,d,dt,mod;
211: UM wf,wdf,ws,wt,wgcd,mf,mgcd;
212: UM *l;
213: struct oDUM *dc;
214: ML tp;
215:
216: n = UDEG(f);
217: wf = W_UMALLOC(n);
218: wdf = W_UMALLOC(n);
219: ws = W_UMALLOC(n);
220: wt = W_UMALLOC(n);
221: wgcd = W_UMALLOC(n);
222:
223: mf = W_UMALLOC(n);
224: mgcd = W_UMALLOC(n);
225:
226: for ( j = 0, d = n; j < count && d; ) {
1.5 noro 227: m = get_lprime(index++);
1.1 noro 228: if ( rem(NM((Q)COEF(DC(f))),m) == 0 ) continue;
229:
230: ptoum(m,f,wf);
231: diffum(m,wf,wdf);
232: cpyum(wf,wt); cpyum(wdf,ws);
233: gcdum(m,wt,ws,wgcd);
234: dt = DEG(wgcd);
235:
236: if ( dt < d ) {
237: d = dt;
238: mod = m;
239: cpyum(wf,mf); cpyum(wgcd,mgcd);
240: }
241: j++;
242: }
243: *nindex = index;
244:
245: sqfrummain(mod,mf,mgcd,&dc);
246: *dcr = dc;
247:
248: for ( n = 0; dc[n].f; n++ );
249: *pl = tp = MLALLOC(n+1);
250: tp->n = n;
251: tp->mod = mod;
252:
253: for ( i = 0, l = (UM *)COEF(tp); dc[i].f; i++ ) {
254: l[i] = UMALLOC(DEG(dc[i].f)*dc[i].n);
255: pwrum(mod,dc[i].f,dc[i].n,l[i]);
256: }
257: l[i] = 0;
258: }
259:
260: void sqfrummain(mod,p,gcd,dcp)
261: int mod;
262: UM p,gcd;
263: struct oDUM **dcp;
264: {
265: int i,j,n;
266: UM wp,wdp,wc,wd,ws,wt,wq;
267: struct oDUM *dc;
268: UM *f;
269:
270: i = DEG(p);
271:
272: wp = W_UMALLOC(i);
273: wdp = W_UMALLOC(i);
274: wt = W_UMALLOC(i);
275: ws = W_UMALLOC(i);
276: wc = W_UMALLOC(i);
277: wd = W_UMALLOC(i);
278: wq = W_UMALLOC(i);
279:
280: f = (UM *) ALLOCA((i+2)*sizeof(UM));
281:
282: cpyum(p,wp);
283: diffum(mod,wp,wdp);
284:
285: cpyum(wp,wt);
286: divum(mod,wt,gcd,wc);
287:
288: cpyum(wdp,wt);
289: divum(mod,wt,gcd,ws);
290:
291: diffum(mod,wc,wt);
292: subum(mod,ws,wt,wd);
293:
294: for ( i = 1; DEG(wd) >= 0; i++ ) {
295: cpyum(wc,ws); cpyum(wd,wt);
296: gcdum(mod,ws,wt,wq);
297: if ( DEG(wq) > 0 ) {
298: f[i] = UMALLOC(DEG(wq));
299: cpyum(wq,f[i]);
300:
301: cpyum(wc,ws);
302: divum(mod,ws,f[i],wc);
303: divum(mod,wd,f[i],ws);
304: diffum(mod,wc,wt);
305: subum(mod,ws,wt,wd);
306: } else {
307: f[i] = 0;
308: cpyum(wd,ws);
309: diffum(mod,wc,wt);
310: subum(mod,ws,wt,wd);
311: }
312:
313: }
314:
315: if ( DEG(wc) > 0 ) {
316: DEG(wq) = 0;
317: COEF(wq)[0] = invm(COEF(wc)[DEG(wc)],mod);
318: f[i] = UMALLOC(DEG(wc));
319: mulum(mod,wc,wq,f[i]);
320: f[i+1] = 0;
321: n = i + 1;
322: } else {
323: f[i] = 0;
324: n = i;
325: }
326:
327: for ( i = 1, j = 0; i < n; i++ )
328: if ( f[i] ) j++;
329:
330: *dcp = dc = (struct oDUM *) CALLOC(j+1,sizeof(struct oDUM));
331:
332: for ( i = 1, j = 0; i < n; i++ )
333: if ( f[i] ) {
334: dc[j].n = i;
335: dc[j].f = f[i];
336: j++;
337: }
338: dc[j].n = 0;
339: dc[j].f = 0;
340: }
341:
342: void cpyum(p1,p2)
343: UM p1,p2;
344: {
345: register int *c1,*c2,i;
346:
347: for ( i = DEG(p2) = DEG(p1), c1 = COEF(p1), c2 = COEF(p2);
348: i >= 0; i-- )
349: c2[i] = c1[i];
350: }
351:
1.7 ! noro 352: void clearum(p,n)
! 353: UM p;
! 354: int n;
! 355: {
! 356: DEG(p) = -1;
! 357: bzero(COEF(p),(n+1)*sizeof(int));
! 358: }
! 359:
1.1 noro 360: void degum(f,n)
361: UM f;
362: int n;
363: {
364: register int i,*c;
365:
366: for ( i = n, c = COEF(f); ( i >= 0 ) && ( c[i] == 0 ); i-- );
367: DEG(f) = i;
368: }
369:
370: int deg(v,p)
371: V v;
372: P p;
373: {
374: if ( !p )
375: return ( -1 );
376: else if ( NUM(p) )
377: return ( 0 );
378: else if ( VR(p) != v )
379: return ( 0 );
380: else if ( PL(NM(DEG(DC(p)))) > 1 ) {
381: error("degree too large");
382: return ( -1 );
383: } else
384: return ( UDEG(p) );
385: }
386:
387: LUM LUMALLOC(n,bound)
388: int n,bound;
389: {
390: LUM p;
391: int **c;
392: int i;
393:
394: p = (LUM)MALLOC(TRUESIZE(oLUM,n,int *));
395: DEG(p) = n;
396: for ( i = 0, c = (int **)COEF(p); i <= n; i++ ) {
397: c[i] = (int *)MALLOC_ATOMIC((bound+1)*sizeof(int));
398: bzero((char *)c[i],(bound+1)*sizeof(int));
1.6 noro 399: }
400: return p;
401: }
402:
1.7 ! noro 403: /* n = deg in x, bound = deg in y, c[i] <-> the coef of y^i (poly in x) */
! 404:
1.6 noro 405: BM BMALLOC(n,bound)
406: int n,bound;
407: {
408: BM p;
409: UM *c;
410: int i;
411:
1.7 ! noro 412: p = (BM)MALLOC(TRUESIZE(oBM,bound,UM));
! 413: DEG(p) = bound;
! 414: for ( i = 0, c = (UM *)COEF(p); i < bound; i++ ) {
! 415: c[i] = UMALLOC(n);
1.6 noro 416: DEG(c[i]) = -1;
1.7 ! noro 417: bzero((char *)COEF(c[i]),(n+1)*sizeof(int));
1.1 noro 418: }
419: return p;
420: }
421:
422: void mullum(mod,n,f1,f2,fr)
423: int mod,n;
424: LUM f1,f2,fr;
425: {
426: int max;
427: register int i,j,**p1,**p2,*px;
428: int *w,*w1,*w2;
429:
430: p1 = (int **)COEF(f1); p2 = (int **)COEF(f2);
431: w = W_ALLOC(2*(n+1)); w1 = W_ALLOC(DEG(f1)); w2 = W_ALLOC(DEG(f2));
432: for ( i = DEG(f1); i >= 0; i-- ) {
433: for ( j = n - 1, px = p1[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- );
434: w1[i] = ( j == -1 ? 0 : 1 );
435: }
436: for ( i = DEG(f2); i >= 0; i-- ) {
437: for ( j = n - 1, px = p2[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- );
438: w2[i] = ( j == -1 ? 0 : 1 );
439: }
440: for ( j = DEG(fr) = DEG(f1) + DEG(f2); j >= 0; j-- ) {
441: for ( i = n - 1, px = COEF(fr)[j]; i >= 0; i-- )
442: px[i] = 0;
443: for ( max = MIN(DEG(f1),j), i = MAX(0,j-DEG(f2)); i <= max; i++ )
444: if ( w1[i] != 0 && w2[j - i] != 0 ) {
445: mulpadic(mod,n,p1[i],p2[j - i],w); addpadic(mod,n,w,px);
446: }
447: }
448: }
449:
450: void cpylum(bound,p,r)
451: int bound;
452: LUM p,r;
453: {
454: register int i,j;
455: register int **pp,**ppr;
456:
457: DEG(r) = DEG(p);
458: for ( i = 0, pp = COEF(p), ppr = COEF(r);
459: i <= DEG(p); i++ )
460: for ( j = 0; j < bound; j++ )
461: ppr[i][j] = pp[i][j];
1.7 ! noro 462: }
! 463:
! 464: int isequalum(f1,f2)
! 465: UM f1,f2;
! 466: {
! 467: int i;
! 468:
! 469: if ( DEG(f1) < 0 )
! 470: if ( DEG(f2) < 0 )
! 471: return 1;
! 472: else
! 473: return 0;
! 474: else if ( DEG(f2) < 0 )
! 475: return 0;
! 476: else {
! 477: if ( DEG(f1) != DEG(f2) )
! 478: return 0;
! 479: for ( i = 0; i <= DEG(f1); i++ )
! 480: if ( COEF(f1)[i] != COEF(f2)[i] )
! 481: break;
! 482: if ( i < DEG(f1) )
! 483: return 0;
! 484: else
! 485: return 1;
! 486: }
1.1 noro 487: }
488:
489: void pwrlum(mod,bound,p,n,r)
490: int mod,bound,n;
491: LUM p,r;
492: {
493: LUM t,s;
494:
495: if ( n == 0 ) {
496: DEG(r) = 0;
497: COEF(r)[0][0] = 1;
498: } else if ( DEG(p) < 0 )
499: DEG(r) = -1;
500: else if ( n == 1 )
501: cpylum(bound,p,r);
502: else {
503: W_LUMALLOC(DEG(p)*n,bound,t);
504: pwrlum(mod,bound,p,n/2,t);
505: if ( !(n%2) )
506: mullum(mod,bound,t,t,r);
507: else {
508: W_LUMALLOC(DEG(p)*n,bound,s);
509: mullum(mod,bound,t,t,s);
510: mullum(mod,bound,s,p,r);
511: }
512: }
513: }
514:
515: int **almat(n,m)
516: int n,m;
517: {
518: int **mat,i;
519:
520: mat = (int **)MALLOC(n*sizeof(int *));
521: for ( i = 0; i < n; i++ )
522: mat[i] = (int *)CALLOC(m,sizeof(int));
523: return mat;
524: }
525:
526: void mini(mod,f,fr)
527: register int mod;
528: UM f,fr;
529: {
530: register int i,j,**c,*ptr;
531: int d,dr,dm,n;
532: UM w,q;
533:
534: n = DEG(f); c = (int **)ALLOCA(n*sizeof(int *));
535: for ( i = 0; i < n; i++ ) {
536: c[i] = (int *)ALLOCA(n*sizeof(int));
537: bzero((char *)c[i],(int)(n*sizeof(int)));
538: }
539: w = W_UMALLOC( mod + n + 10 ); q = W_UMALLOC( mod + n + 10 );
540: for ( i = 1; ( d = ( mod * i ) ) < n; i++ ) c[d][i - 1] = 1;
541: DEG(w) = d;
542: for ( j = 0; j < d; j++ )
543: COEF(w)[j] = 0;
544: COEF(w)[d] = 1;
545: for ( ; (i < n) && ((dr = divum(mod,w,f,q)) >= 0); i++ ) {
546: for ( j = dr; j >= 0; j-- )
547: COEF(w)[j + mod] = c[j][i - 1] = COEF(w)[j];
548: for ( j = mod - 1; j >= 0; j-- )
549: COEF(w)[j] = 0;
550: DEG(w) = dr + mod;
551: }
552: for ( i = 1; i < n; i++ )
553: c[i][i - 1] = ( c[i][i - 1] + mod - 1 ) % mod;
554: if ( ( dm = minimain(mod,n,n - 1,c) ) != -1 )
555: for ( i = 0, ptr = COEF(fr), ptr[0] = 0; i <= dm; i++ )
556: ptr[i + 1] = c[0][i];
557: else
558: COEF(fr)[0] = 1;
559: DEG(fr) = dm + 1;
560: }
561:
562: int minimain(mod,n,m,c)
563: register int mod;
564: int n,m;
565: register int **c;
566: {
567: register int *ptr,*ci,*p;
568: register int i,l,a,j,b,inv;
569: int *tmp;
570:
571: for ( j = 0; j < m; j++ ) {
572: for ( i = j; (n > i) && !c[i][j]; i++ );
573: if ( i == n ) {
574: for ( i = j, j = j - 1; j >= 0; j-- )
575: c[0][j] = c[j][i];
576: c[0][i] = mod - 1;
577: return( i );
578: }
579: if ( i != j ) {
580: tmp = c[i]; c[i] = c[j]; c[j] = tmp;
581: }
582: ptr = c[j]; inv = invm((ptr[j] + mod) % mod,mod);
583: for ( l = j, p = ptr+l; l < m; l++ ) {
584: a = (*p * inv) % mod;
585: *p++ = (a<0?a+mod:a);
586: }
587: for ( i = 0; i < n; i++ )
588: if ( (a = -c[i][j]) && (i != j) ) {
589: for ( l = j+1, p = ptr+l, ci = c[i]+l; l < m; l++ ) {
590: b = (*p++ * a + *ci) % mod;
591: *ci++ = (b<0?b+mod:b);
592: }
593: c[i][j] = 0;
594: }
595: }
596: return (-1);
597: }
598:
1.4 noro 599: #if defined(__GNUC__)
1.1 noro 600: const
601: #endif
602: int sprime[] = {
603: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,
604: 53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,
605: 127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,
606: 199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,
607: 283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,
608: 383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,
609: 467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,
610: 577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,
611: 661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,
612: 769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,
613: 877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,
614: 983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,
615: 1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,
616: 1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,
617: 1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,
618: 1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,
619: 1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,
620: 1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,
621: 1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,
622: 1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,
623: 1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,
624: 2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,
625: 2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,
626: 2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,
627: 2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,
628: 2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,
629: 2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,
630: 2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,
631: 2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,
632: 3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,
633: 3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,
634: 3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,
635: 3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,
636: 3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,
637: 3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,
638: 3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,
639: 3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,
640: 4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,
641: 4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,
642: 4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,
643: 4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,
644: 4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,
645: 4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,
646: 4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,
647: 4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,
648: 5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,
649: 5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,
650: 5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,
651: 5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,
652: 5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,
653: 5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,
654: 5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,
655: 5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,
656: 6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,
657: 6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,
658: 6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,
659: 6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,
660: 6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,
661: 6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,
662: 6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,
663: 7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,
664: 7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,
665: 7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,
666: 7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,
667: 7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,
668: 7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,
669: 7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,
670: 7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,
671: 8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,
672: 8263,8269,8273,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387,
673: 8389,8419,8423,8429,8431,8443,8447,8461,8467,8501,8513,8521,8527,8537,8539,
674: 8543,8563,8573,8581,8597,8599,8609,8623,8627,8629,8641,8647,8663,8669,8677,
675: 8681,8689,8693,8699,8707,8713,8719,8731,8737,8741,8747,8753,8761,8779,8783,
676: 8803,8807,8819,8821,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923,8929,
677: 8933,8941,8951,8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049,
678: 9059,9067,9091,9103,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187,9199,
679: 9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337,
680: 9341,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439,
681: 9461,9463,9467,9473,9479,9491,9497,9511,9521,9533,9539,9547,9551,9587,9601,
682: 9613,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721,9733,
683: 9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851,
684: 9857,9859,9871,9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973,10007,
685: 10009,10037,10039,10061,10067,10069,10079,10091,10093,10099,
686: 10103,10111,10133,10139,10141,10151,10159,10163,10169,10177,
687: 10181,10193,10211,10223,10243,10247,10253,10259,10267,10271,
688: 10273,10289,10301,10303,10313,10321,10331,10333,10337,10343,
689: 10357,10369,10391,10399,10427,10429,10433,10453,10457,10459,
690: 10463,10477,10487,10499,10501,10513,10529,10531,10559,10567,
691: 10589,10597,10601,10607,10613,10627,10631,10639,10651,10657,
692: 10663,10667,10687,10691,10709,10711,10723,10729,10733,10739,
693: 10753,10771,10781,10789,10799,10831,10837,10847,10853,10859,
694: 10861,10867,10883,10889,10891,10903,10909,10937,10939,10949,
695: 10957,10973,10979,10987,10993,11003,11027,11047,11057,11059,
696: 11069,11071,11083,11087,11093,11113,11117,11119,11131,11149,
697: 11159,11161,11171,11173,11177,11197,11213,11239,11243,11251,
698: 11257,11261,11273,11279,11287,11299,11311,11317,11321,11329,
699: 11351,11353,11369,11383,11393,11399,11411,11423,11437,11443,
700: 11447,11467,11471,11483,11489,11491,11497,11503,11519,11527,
701: 11549,11551,11579,11587,11593,11597,11617,11621,11633,11657,
702: 11677,11681,11689,11699,11701,11717,11719,11731,11743,11777,
703: 11779,11783,11789,11801,11807,11813,11821,11827,11831,11833,
704: 11839,11863,11867,11887,11897,11903,11909,11923,11927,11933,
705: 11939,11941,11953,11959,11969,11971,11981,11987,12007,12011,
706: 12037,12041,12043,12049,12071,12073,12097,12101,12107,12109,
707: 12113,12119,12143,12149,12157,12161,12163,12197,12203,12211,
708: 12227,12239,12241,12251,12253,12263,12269,12277,12281,12289,
709: 12301,12323,12329,12343,12347,12373,12377,12379,12391,12401,
710: 12409,12413,12421,12433,12437,12451,12457,12473,12479,12487,
711: 12491,12497,12503,12511,12517,12527,12539,12541,12547,12553,
712: 12569,12577,12583,12589,12601,12611,12613,12619,12637,12641,
713: 12647,12653,12659,12671,12689,12697,12703,12713,12721,12739,
714: 12743,12757,12763,12781,12791,12799,12809,12821,12823,12829,
715: 12841,12853,12889,12893,12899,12907,12911,12917,12919,12923,
716: 12941,12953,12959,12967,12973,12979,12983,13001,13003,13007,
717: 13009,13033,13037,13043,13049,13063,13093,13099,13103,13109,
718: 13121,13127,13147,13151,13159,13163,13171,13177,13183,13187,
719: 13217,13219,13229,13241,13249,13259,13267,13291,13297,13309,
720: 13313,13327,13331,13337,13339,13367,13381,13397,13399,13411,
721: 13417,13421,13441,13451,13457,13463,13469,13477,13487,13499,
722: 13513,13523,13537,13553,13567,13577,13591,13597,13613,13619,
723: 13627,13633,13649,13669,13679,13681,13687,13691,13693,13697,
724: 13709,13711,13721,13723,13729,13751,13757,13759,13763,13781,
725: 13789,13799,13807,13829,13831,13841,13859,13873,13877,13879,
726: 13883,13901,13903,13907,13913,13921,13931,13933,13963,13967,
727: 13997,13999,14009,14011,14029,14033,14051,14057,14071,14081,
728: 14083,14087,14107,14143,14149,14153,14159,14173,14177,14197,
729: 14207,14221,14243,14249,14251,14281,14293,14303,14321,14323,
730: 14327,14341,14347,14369,14387,14389,14401,14407,14411,14419,
731: 14423,14431,14437,14447,14449,14461,14479,14489,14503,14519,
732: 14533,14537,14543,14549,14551,14557,14561,14563,14591,14593,
733: 14621,14627,14629,14633,14639,14653,14657,14669,14683,14699,
734: 14713,14717,14723,14731,14737,14741,14747,14753,14759,14767,
735: 14771,14779,14783,14797,14813,14821,14827,14831,14843,14851,
736: 14867,14869,14879,14887,14891,14897,14923,14929,14939,14947,
737: 14951,14957,14969,14983,15013,15017,15031,15053,15061,15073,
738: 15077,15083,15091,15101,15107,15121,15131,15137,15139,15149,
739: 15161,15173,15187,15193,15199,15217,15227,15233,15241,15259,
740: 15263,15269,15271,15277,15287,15289,15299,15307,15313,15319,
741: 15329,15331,15349,15359,15361,15373,15377,15383,15391,15401,
742: 15413,15427,15439,15443,15451,15461,15467,15473,15493,15497,
743: 15511,15527,15541,15551,15559,15569,15581,15583,15601,15607,
744: 15619,15629,15641,15643,15647,15649,15661,15667,15671,15679,
745: 15683,15727,15731,15733,15737,15739,15749,15761,15767,15773,
746: 15787,15791,15797,15803,15809,15817,15823,15859,15877,15881,
747: 15887,15889,15901,15907,15913,15919,15923,15937,15959,15971,
748: 15973,15991,16001,16007,16033,16057,16061,16063,16067,16069,
749: 16073,16087,16091,16097,16103,16111,16127,16139,16141,16183,
750: 16187,16189,16193,16217,16223,16229,16231,16249,16253,16267,
751: 16273,16301,16319,16333,16339,16349,16361,16363,16369,16381,
752: 0
753: };
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