OpenXM_contrib2/asir2000/engine/M.c - diff

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Diff for /OpenXM_contrib2/asir2000/engine/M.c between version 1.3 and 1.10

-version 1.3, 2000/08/22 05:04:04
+version 1.10, 2018/03/29 01:32:51
 Line 45
 Line 45
 Line 45
   * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
   * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
   *
-  * $OpenXM: OpenXM_contrib2/asir2000/engine/M.c,v 1.2 2000/08/21 08:31:25 noro Exp $
+  * $OpenXM: OpenXM_contrib2/asir2000/engine/M.c,v 1.9 2001/10/09 01:36:10 noro Exp $
  */
  #include "ca.h"
  #include "base.h"
- void addum(mod,p1,p2,pr)
+ void addum(int mod,UM p1,UM p2,UM pr)
- int mod;
- UM p1,p2,pr;
  {
-         register int *c1,*c2,*cr,i,dmax,dmin;
+   register int *c1,*c2,*cr,i,dmax,dmin;
-         if ( DEG(p1) == -1 ) {
+   if ( DEG(p1) == -1 ) {
-                 cpyum(p2,pr);
+     cpyum(p2,pr);
-                 return;
+     return;
-         }
+   }
-         if ( DEG(p2) == -1 ) {
+   if ( DEG(p2) == -1 ) {
-                 cpyum(p1,pr);
+     cpyum(p1,pr);
-                 return;
+     return;
-         }
+   }
-         if ( DEG(p1) >= DEG(p2) ) {
+   if ( DEG(p1) >= DEG(p2) ) {
-                 c1 = COEF(p1); c2 = COEF(p2); dmax = DEG(p1); dmin = DEG(p2);
+     c1 = COEF(p1); c2 = COEF(p2); dmax = DEG(p1); dmin = DEG(p2);
-         } else {
+   } else {
-                 c1 = COEF(p2); c2 = COEF(p1); dmax = DEG(p2); dmin = DEG(p1);
+     c1 = COEF(p2); c2 = COEF(p1); dmax = DEG(p2); dmin = DEG(p1);
-         }
+   }
-         for ( i = 0, cr = COEF(pr); i <= dmin; i++ )
+   for ( i = 0, cr = COEF(pr); i <= dmin; i++ )
-                 cr[i] = ( c1[i] + c2[i] ) % mod;
+     cr[i] = ( c1[i] + c2[i] ) % mod;
-         for ( ; i <= dmax; i++ )
+   for ( ; i <= dmax; i++ )
-                 cr[i] = c1[i];
+     cr[i] = c1[i];
-         if ( dmax == dmin )
+   if ( dmax == dmin )
-                 degum(pr,dmax);
+     degum(pr,dmax);
-         else
+   else
-                 DEG(pr) = dmax;
+     DEG(pr) = dmax;
  }
- void subum(mod,p1,p2,pr)
+ void subum(int mod,UM p1,UM p2,UM pr)
- int mod;
- UM p1,p2,pr;
  {
-         register int *c1,*c2,*cr,i;
+   register int *c1,*c2,*cr,i;
-         int dmax,dmin;
+   int dmax,dmin;
-         if ( DEG(p1) == -1 ) {
+   if ( DEG(p1) == -1 ) {
-                 for ( i = DEG(pr) = DEG(p2), c2 = COEF(p2), cr = COEF(pr);
+     for ( i = DEG(pr) = DEG(p2), c2 = COEF(p2), cr = COEF(pr);
-                           i >= 0; i-- )
+         i >= 0; i-- )
-                         cr[i] = ( mod - c2[i] ) % mod;
+       cr[i] = ( mod - c2[i] ) % mod;
-                 return;
+     return;
-         }
+   }
-         if ( DEG(p2) == -1 ) {
+   if ( DEG(p2) == -1 ) {
-                 cpyum(p1,pr);
+     cpyum(p1,pr);
-                 return;
+     return;
-         }
+   }
-         c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr);
+   c1 = COEF(p1); c2 = COEF(p2); cr = COEF(pr);
-         if ( DEG(p1) >= DEG(p2) ) {
+   if ( DEG(p1) >= DEG(p2) ) {
-                 dmax = DEG(p1); dmin = DEG(p2);
+     dmax = DEG(p1); dmin = DEG(p2);
-                 for ( i = 0; i <= dmin; i++ )
+     for ( i = 0; i <= dmin; i++ )
-                         cr[i] = ( c1[i] + mod - c2[i] ) % mod;
+       cr[i] = ( c1[i] + mod - c2[i] ) % mod;
-                 for ( ; i <= dmax; i++ )
+     for ( ; i <= dmax; i++ )
-                         cr[i] = c1[i];
+       cr[i] = c1[i];
-         } else {
+   } else {
-                 dmax = DEG(p2); dmin = DEG(p1);
+     dmax = DEG(p2); dmin = DEG(p1);
-                 for ( i = 0; i <= dmin; i++ )
+     for ( i = 0; i <= dmin; i++ )
-                         cr[i] = ( c1[i] + mod - c2[i] ) % mod;
+       cr[i] = ( c1[i] + mod - c2[i] ) % mod;
-                 for ( ; i <= dmax; i++ )
+     for ( ; i <= dmax; i++ )
-                         cr[i] = ( mod - c2[i] ) % mod;
+       cr[i] = ( mod - c2[i] ) % mod;
-         }
+   }
-         if ( dmax == dmin )
+   if ( dmax == dmin )
-                 degum(pr,dmax);
+     degum(pr,dmax);
-         else
+   else
-                 DEG(pr) = dmax;
+     DEG(pr) = dmax;
  }
- void pwrum(mod,p,e,pr)
+ void pwrum(int mod,UM p,int e,UM pr)
- int mod,e;
- UM p,pr;
  {
-         UM wt,ws;
+   UM wt,ws;
-         if ( e == 0 ) {
+   if ( e == 0 ) {
-                 DEG(pr) = 0; COEF(pr)[0] = 1;
+     DEG(pr) = 0; COEF(pr)[0] = 1;
-         } else if ( DEG(p) < 0 )
+   } else if ( DEG(p) < 0 )
-                 DEG(pr) = -1;
+     DEG(pr) = -1;
-         else if ( e == 1 )
+   else if ( e == 1 )
-                 cpyum(p,pr);
+     cpyum(p,pr);
-         else if ( DEG(p) == 0 ) {
+   else if ( DEG(p) == 0 ) {
-                 DEG(pr) = 0; COEF(pr)[0] = pwrm(mod,COEF(p)[0],e);
+     DEG(pr) = 0; COEF(pr)[0] = pwrm(mod,COEF(p)[0],e);
-         } else {
+   } else {
-                 wt = W_UMALLOC(DEG(p)*e); ws = W_UMALLOC(DEG(p)*e);
+     wt = W_UMALLOC(DEG(p)*e); ws = W_UMALLOC(DEG(p)*e);
-                 pwrum(mod,p,e/2,wt);
+     pwrum(mod,p,e/2,wt);
-                 if ( !(e%2) )
+     if ( !(e%2) )
-                         mulum(mod,wt,wt,pr);
+       mulum(mod,wt,wt,pr);
-                 else {
+     else {
-                         mulum(mod,wt,wt,ws); mulum(mod,ws,p,pr);
+       mulum(mod,wt,wt,ws); mulum(mod,ws,p,pr);
-                 }
+     }
-         }
+   }
  }
- void gcdum(mod,p1,p2,pr)
+ void gcdum(int mod,UM p1,UM p2,UM pr)
- register int mod;
- UM p1,p2,pr;
  {
-         register int inv;
+   register int inv;
-         UM t1,t2,q,tum;
+   UM t1,t2,q,tum;
-         int drem;
+   int drem;
-         if ( DEG(p1) < 0 )
+   if ( DEG(p1) < 0 )
-                 cpyum(p2,pr);
+     cpyum(p2,pr);
-         else if ( DEG(p2) < 0 )
+   else if ( DEG(p2) < 0 )
-                 cpyum(p1,pr);
+     cpyum(p1,pr);
-         else {
+   else {
-                 if ( DEG(p1) >= DEG(p2) ) {
+     if ( DEG(p1) >= DEG(p2) ) {
-                         t1 = p1; t2 = p2;
+       t1 = p1; t2 = p2;
-                 } else {
+     } else {
-                         t1 = p2; t2 = p1;
+       t1 = p2; t2 = p1;
-                 }
+     }
-                 q = W_UMALLOC(DEG(t1));
+     q = W_UMALLOC(DEG(t1));
-                 while ( ( drem = divum(mod,t1,t2,q) ) >= 0 ) {
+     while ( ( drem = divum(mod,t1,t2,q) ) >= 0 ) {
-                         tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem;
+       tum = t1; t1 = t2; t2 = tum; DEG(t2) = drem;
-                 }
+     }
-                 inv = invm(COEF(t2)[DEG(t2)],mod);
+     inv = invm(COEF(t2)[DEG(t2)],mod);
-                 mulsum(mod,t2,inv,pr);
+     mulsum(mod,t2,inv,pr);
-         }
+   }
  }
- void eucum(mod,f1,f2,a,b)
+ void eucum(int mod,UM f1,UM f2,UM a,UM b)
- register int mod;
- UM f1,f2,a,b;
  {
-         UM g1,g2,a1,a2,a3,wm,q,tum;
+   UM g1,g2,a1,a2,a3,wm,q,tum;
-         int d,dr;
+   int d,dr;
-         d = DEG(f1) + DEG(f2) + 10;
+   d = DEG(f1) + DEG(f2) + 10;
-         g1 = W_UMALLOC(d); g2 = W_UMALLOC(d); a1 = W_UMALLOC(d);
+   g1 = W_UMALLOC(d); g2 = W_UMALLOC(d); a1 = W_UMALLOC(d);
-         a2 = W_UMALLOC(d); a3 = W_UMALLOC(d); wm = W_UMALLOC(d);
+   a2 = W_UMALLOC(d); a3 = W_UMALLOC(d); wm = W_UMALLOC(d);
-         q = W_UMALLOC(d);
+   q = W_UMALLOC(d);
-         DEG(a1) = 0; COEF(a1)[0] = 1; DEG(a2) = -1;
+   DEG(a1) = 0; COEF(a1)[0] = 1; DEG(a2) = -1;
-         cpyum(f1,g1); cpyum(f2,g2);
+   cpyum(f1,g1); cpyum(f2,g2);
-         while ( 1 ) {
+   while ( 1 ) {
-                 dr = divum(mod,g1,g2,q); tum = g1; g1 = g2; g2 = tum;
+     dr = divum(mod,g1,g2,q); tum = g1; g1 = g2; g2 = tum;
-                 if ( ( DEG(g2) = dr ) == -1 )
+     if ( ( DEG(g2) = dr ) == -1 )
-                         break;
+       break;
-                 mulum(mod,a2,q,wm); subum(mod,a1,wm,a3); dr = divum(mod,a3,f2,q);
+     mulum(mod,a2,q,wm); subum(mod,a1,wm,a3); dr = divum(mod,a3,f2,q);
-                 tum = a1; a1 = a2; a2 = a3; a3 = tum; DEG(a3) = dr;
+     tum = a1; a1 = a2; a2 = a3; a3 = tum; DEG(a3) = dr;
-         }
+   }
-         if ( COEF(g1)[0] != 1 )
+   if ( COEF(g1)[0] != 1 )
-                 mulsum(mod,a2,invm(COEF(g1)[0],mod),a);
+     mulsum(mod,a2,invm(COEF(g1)[0],mod),a);
-         else
+   else
-                 cpyum(a2,a);
+     cpyum(a2,a);
-         mulum(mod,a,f1,wm);
+   mulum(mod,a,f1,wm);
-         if ( DEG(wm) >= 0 )
+   if ( DEG(wm) >= 0 )
-                 COEF(wm)[0] = ( COEF(wm)[0] + mod - 1 ) % mod;
+     COEF(wm)[0] = ( COEF(wm)[0] + mod - 1 ) % mod;
-         else {
+   else {
-                 DEG(wm) = 0; COEF(wm)[0] = mod - 1;
+     DEG(wm) = 0; COEF(wm)[0] = mod - 1;
-         }
+   }
-         divum(mod,wm,f2,q); mulsum(mod,q,mod-1,b);
+   divum(mod,wm,f2,q); mulsum(mod,q,mod-1,b);
+ #if 0
+   t1 = W_UMALLOC(d);
+   t2 = W_UMALLOC(d);
+   t3 = W_UMALLOC(d);
+   mulum(mod,a,f1,t1);
+   mulum(mod,b,f2,t2);
+   addum(mod,t1,t2,t3);
+ #endif
  }
- void sqfrum(index,count,f,nindex,dcr,pl)
+ void eucum2(int mod,UM f1,UM f2,UM a,UM b)
- int index,count,*nindex;
- P f;
- struct oDUM **dcr;
- ML *pl;
  {
-         int i,j,m,n,d,dt,mod;
+   UM gk,gk1,gk2,ak,ak1,ak2,bk,bk1,bk2,q,t,wm1,wm2,wz;
-         UM wf,wdf,ws,wt,wgcd,mf,mgcd;
+   int d,inv;
-         UM *l;
+   UM t1,t2;
-         struct oDUM *dc;
-         ML tp;
-         n = UDEG(f);
+   d = 2*(DEG(f1) + DEG(f2));
-         wf = W_UMALLOC(n);
+   gk = W_UMALLOC(d); gk1 = W_UMALLOC(d); gk2 = W_UMALLOC(d);
-         wdf = W_UMALLOC(n);
+   ak = W_UMALLOC(d); ak1 = W_UMALLOC(d); ak2 = W_UMALLOC(d);
-         ws = W_UMALLOC(n);
+   bk = W_UMALLOC(d); bk1 = W_UMALLOC(d); bk2 = W_UMALLOC(d);
-         wt = W_UMALLOC(n);
+   q = W_UMALLOC(d); wm1 = W_UMALLOC(d); wm2 = W_UMALLOC(d);
-         wgcd = W_UMALLOC(n);
+   wz = W_UMALLOC(d);
+   t1 = UMALLOC(1000);
+   t2 = UMALLOC(1000);
+   cpyum(f1,t1);
+   cpyum(f2,t2);
-         mf = W_UMALLOC(n);
+   DEG(ak) = 0; COEF(ak)[0] = 1;
-         mgcd = W_UMALLOC(n);
+   DEG(ak1) = -1;
+   DEG(bk) = -1;
+   DEG(bk1) = 0; COEF(bk1)[0] = 1;
-         for ( j = 0, d = n; j < count && d; ) {
+   cpyum(f1,gk); cpyum(f2,gk1);
-                 m = lprime[index++];
-                 if ( !m )
-                         error("sqfrum : lprime[] exhausted.");
-                 if ( rem(NM((Q)COEF(DC(f))),m) == 0 ) continue;
-                 ptoum(m,f,wf);
+   while ( 1 ) {
-                 diffum(m,wf,wdf);
+     /* ak*f1+bk*f2 = gk, ak1*f1+bk1*f2 = gk1 */
-                 cpyum(wf,wt); cpyum(wdf,ws);
+     cpyum(gk,gk2);
-                 gcdum(m,wt,ws,wgcd);
+     DEG(gk2) = divum(mod,gk2,gk1,q);
-                 dt = DEG(wgcd);
+     /* gk2 = gk - q*gk1 */
+     if ( DEG(gk2) == -1 )
+       break;
+     /* ak2 = ak - q*ak1, bk2 = bk - q*bk1 */
+     mulum(mod,ak1,q,wm1); subum(mod,ak,wm1,ak2);
+     mulum(mod,bk1,q,wm1); subum(mod,bk,wm1,bk2);
-                 if ( dt < d ) {
+     /* shift */
-                         d = dt;
+     t = ak; ak = ak1; ak1 = ak2; ak2 = t;
-                         mod = m;
+     t = bk; bk = bk1; bk1 = bk2; bk2 = t;
-                         cpyum(wf,mf); cpyum(wgcd,mgcd);
+     t = gk; gk = gk1; gk1 = gk2; gk2 = t;
-                 }
+   }
-                 j++;
+   /* ak1*f1+bk1*f2 = gk1 = GCD(f1,f2) */
-         }
+   mulum(mod,ak1,t1,wm1);
-         *nindex = index;
+   mulum(mod,bk1,t2,wm2);
+   addum(mod,wm1,wm2,wz);
+   if ( DEG(wz) != 0 )
+     error("euc 1");
-         sqfrummain(mod,mf,mgcd,&dc);
+   DEG(ak1) = divum(mod,ak1,f2,q);
-         *dcr = dc;
+   DEG(bk1) = divum(mod,bk1,f1,q);
+   mulum(mod,ak1,f1,wm1);
+   mulum(mod,bk1,f2,wm2);
+   addum(mod,wm1,wm2,wz);
+   if ( DEG(wz) != 0 )
+     error("euc 2");
-         for ( n = 0; dc[n].f; n++ );
-         *pl = tp = MLALLOC(n+1);
-         tp->n = n;
-         tp->mod = mod;
-         for ( i = 0, l = (UM *)COEF(tp); dc[i].f; i++ ) {
+   if ( COEF(wz)[0] != 1 ) {
-                 l[i] = UMALLOC(DEG(dc[i].f)*dc[i].n);
+     inv = invm(COEF(wz)[0],mod);
-                 pwrum(mod,dc[i].f,dc[i].n,l[i]);
+     mulsum(mod,ak1,inv,a);
-         }
+     mulsum(mod,bk1,inv,b);
-         l[i] = 0;
+   } else {
+     cpyum(ak1,a);
+     cpyum(bk1,b);
+   }
  }
- void sqfrummain(mod,p,gcd,dcp)
+ void sqfrum(int index,int count,P f,int *nindex,struct oDUM **dcr,ML *pl)
- int mod;
- UM p,gcd;
- struct oDUM **dcp;
  {
-         int i,j,n;
+   int i,j,m,n,d,dt,mod;
-         UM wp,wdp,wc,wd,ws,wt,wq;
+   UM wf,wdf,ws,wt,wgcd,mf,mgcd;
-         struct oDUM *dc;
+   UM *l;
-         UM *f;
+   struct oDUM *dc;
+   ML tp;
-         i = DEG(p);
+   n = UDEG(f);
+   wf = W_UMALLOC(n);
+   wdf = W_UMALLOC(n);
+   ws = W_UMALLOC(n);
+   wt = W_UMALLOC(n);
+   wgcd = W_UMALLOC(n);
-         wp = W_UMALLOC(i);
+   mf = W_UMALLOC(n);
-         wdp = W_UMALLOC(i);
+   mgcd = W_UMALLOC(n);
-         wt = W_UMALLOC(i);
-         ws = W_UMALLOC(i);
-         wc = W_UMALLOC(i);
-         wd = W_UMALLOC(i);
-         wq =  W_UMALLOC(i);
-         f = (UM *) ALLOCA((i+2)*sizeof(UM));
+   for ( j = 0, d = n; j < count && d; ) {
+     m = get_lprime(index++);
+     if ( rem(NM((Q)COEF(DC(f))),m) == 0 ) continue;
-         cpyum(p,wp);
+     ptoum(m,f,wf);
-         diffum(mod,wp,wdp);
+     diffum(m,wf,wdf);
+     cpyum(wf,wt); cpyum(wdf,ws);
+     gcdum(m,wt,ws,wgcd);
+     dt = DEG(wgcd);
-         cpyum(wp,wt);
+     if ( dt < d ) {
-         divum(mod,wt,gcd,wc);
+       d = dt;
+       mod = m;
+       cpyum(wf,mf); cpyum(wgcd,mgcd);
+     }
+     j++;
+   }
+   *nindex = index;
-         cpyum(wdp,wt);
+   sqfrummain(mod,mf,mgcd,&dc);
-         divum(mod,wt,gcd,ws);
+   *dcr = dc;
-         diffum(mod,wc,wt);
+   for ( n = 0; dc[n].f; n++ );
-         subum(mod,ws,wt,wd);
+   *pl = tp = MLALLOC(n+1);
+   tp->n = n;
+   tp->mod = mod;
-         for ( i = 1; DEG(wd) >= 0; i++ ) {
+   for ( i = 0, l = (UM *)COEF(tp); dc[i].f; i++ ) {
-                 cpyum(wc,ws); cpyum(wd,wt);
+     l[i] = UMALLOC(DEG(dc[i].f)*dc[i].n);
-                 gcdum(mod,ws,wt,wq);
+     pwrum(mod,dc[i].f,dc[i].n,l[i]);
-                 if ( DEG(wq) > 0 ) {
+   }
-                         f[i] = UMALLOC(DEG(wq));
+   l[i] = 0;
-                         cpyum(wq,f[i]);
+ }
-                         cpyum(wc,ws);
+ void sqfrummain(int mod,UM p,UM gcd,struct oDUM **dcp)
-                         divum(mod,ws,f[i],wc);
+ {
-                         divum(mod,wd,f[i],ws);
+   int i,j,n;
-                         diffum(mod,wc,wt);
+   UM wp,wdp,wc,wd,ws,wt,wq;
-                         subum(mod,ws,wt,wd);
+   struct oDUM *dc;
-                 } else {
+   UM *f;
-                         f[i] = 0;
-                         cpyum(wd,ws);
-                         diffum(mod,wc,wt);
-                         subum(mod,ws,wt,wd);
-                 }
-         }
-         if ( DEG(wc) > 0 ) {
+   i = DEG(p);
-                 DEG(wq) = 0;
-                 COEF(wq)[0] = invm(COEF(wc)[DEG(wc)],mod);
-                 f[i] = UMALLOC(DEG(wc));
-                 mulum(mod,wc,wq,f[i]);
-                 f[i+1] = 0;
-                 n = i + 1;
-         } else {
-                 f[i] = 0;
-                 n = i;
-         }
-         for ( i = 1, j = 0; i < n; i++ )
-                 if ( f[i] ) j++;
-         *dcp = dc = (struct oDUM *) CALLOC(j+1,sizeof(struct oDUM));
+   wp = W_UMALLOC(i);
+   wdp = W_UMALLOC(i);
+   wt = W_UMALLOC(i);
+   ws = W_UMALLOC(i);
+   wc = W_UMALLOC(i);
+   wd = W_UMALLOC(i);
+   wq =  W_UMALLOC(i);
-         for ( i = 1, j = 0; i < n; i++ )
+   f = (UM *) ALLOCA((i+2)*sizeof(UM));
-                 if ( f[i] ) {
-                         dc[j].n = i;
+   cpyum(p,wp);
-                         dc[j].f = f[i];
+   diffum(mod,wp,wdp);
-                         j++;
-                 }
+   cpyum(wp,wt);
-         dc[j].n = 0;
+   divum(mod,wt,gcd,wc);
-         dc[j].f = 0;
+   cpyum(wdp,wt);
+   divum(mod,wt,gcd,ws);
+   diffum(mod,wc,wt);
+   subum(mod,ws,wt,wd);
+   for ( i = 1; DEG(wd) >= 0; i++ ) {
+     cpyum(wc,ws); cpyum(wd,wt);
+     gcdum(mod,ws,wt,wq);
+     if ( DEG(wq) > 0 ) {
+       f[i] = UMALLOC(DEG(wq));
+       cpyum(wq,f[i]);
+       cpyum(wc,ws);
+       divum(mod,ws,f[i],wc);
+       divum(mod,wd,f[i],ws);
+       diffum(mod,wc,wt);
+       subum(mod,ws,wt,wd);
+     } else {
+       f[i] = 0;
+       cpyum(wd,ws);
+       diffum(mod,wc,wt);
+       subum(mod,ws,wt,wd);
+     }
+   }
+   if ( DEG(wc) > 0 ) {
+     DEG(wq) = 0;
+     COEF(wq)[0] = invm(COEF(wc)[DEG(wc)],mod);
+     f[i] = UMALLOC(DEG(wc));
+     mulum(mod,wc,wq,f[i]);
+     f[i+1] = 0;
+     n = i + 1;
+   } else {
+     f[i] = 0;
+     n = i;
+   }
+   for ( i = 1, j = 0; i < n; i++ )
+     if ( f[i] ) j++;
+   *dcp = dc = (struct oDUM *) CALLOC(j+1,sizeof(struct oDUM));
+   for ( i = 1, j = 0; i < n; i++ )
+     if ( f[i] ) {
+       dc[j].n = i;
+       dc[j].f = f[i];
+       j++;
+     }
+   dc[j].n = 0;
+   dc[j].f = 0;
  }
- void cpyum(p1,p2)
+ void cpyum(UM p1,UM p2)
- UM p1,p2;
  {
-         register int *c1,*c2,i;
+   register int *c1,*c2,i;
-         for ( i = DEG(p2) = DEG(p1), c1 = COEF(p1), c2 = COEF(p2);
+   for ( i = DEG(p2) = DEG(p1), c1 = COEF(p1), c2 = COEF(p2);
-                   i >= 0; i-- )
+       i >= 0; i-- )
-                 c2[i] = c1[i];
+     c2[i] = c1[i];
  }
- void degum(f,n)
+ void clearum(UM p,int n)
- UM f;
- int n;
  {
-         register int i,*c;
+   DEG(p) = -1;
+   bzero(COEF(p),(n+1)*sizeof(int));
+ }
-         for ( i = n, c = COEF(f); ( i >= 0 ) && ( c[i] == 0 ); i-- );
+ void degum(UM f,int n)
-         DEG(f) = i;
+ {
+   register int i,*c;
+   for ( i = n, c = COEF(f); ( i >= 0 ) && ( c[i] == 0 ); i-- );
+   DEG(f) = i;
  }
- int deg(v,p)
+ int deg(V v,P p)
- V v;
- P p;
  {
-         if ( !p )
+   if ( !p )
-                 return ( -1 );
+     return ( -1 );
-         else if ( NUM(p) )
+   else if ( NUM(p) )
-                 return ( 0 );
+     return ( 0 );
-         else if ( VR(p) != v )
+   else if ( VR(p) != v )
-                 return ( 0 );
+     return ( 0 );
-         else if ( PL(NM(DEG(DC(p)))) > 1 ) {
+   else if ( PL(NM(DEG(DC(p)))) > 1 ) {
-                 error("degree too large");
+     error("degree too large");
-                 return ( -1 );
+     return ( -1 );
-         } else
+   } else
-                 return ( UDEG(p) );
+     return ( UDEG(p) );
  }
- LUM LUMALLOC(n,bound)
+ LUM LUMALLOC(int n,int bound)
- int n,bound;
  {
-         LUM p;
+   LUM p;
-         int **c;
+   int **c;
-         int i;
+   int i;
-         p = (LUM)MALLOC(TRUESIZE(oLUM,n,int *));
+   p = (LUM)MALLOC(TRUESIZE(oLUM,n,int *));
-         DEG(p) = n;
+   DEG(p) = n;
-         for ( i = 0, c = (int **)COEF(p); i <= n; i++ ) {
+   for ( i = 0, c = (int **)COEF(p); i <= n; i++ ) {
-                 c[i] = (int *)MALLOC_ATOMIC((bound+1)*sizeof(int));
+     c[i] = (int *)MALLOC_ATOMIC((bound+1)*sizeof(int));
-                 bzero((char *)c[i],(bound+1)*sizeof(int));
+     bzero((char *)c[i],(bound+1)*sizeof(int));
-         }
+   }
-         return p;
+   return p;
  }
- void mullum(mod,n,f1,f2,fr)
+ /* dx = deg in x, dy = deg in y, c[i] <-> the coef of y^i (poly in x) */
- int mod,n;
- LUM f1,f2,fr;
+ BM BMALLOC(int dx,int dy)
  {
-         int max;
+   BM p;
-         register int i,j,**p1,**p2,*px;
+   UM *c;
-         int *w,*w1,*w2;
+   int i;
-         p1 = (int **)COEF(f1); p2 = (int **)COEF(f2);
+   p = (BM)MALLOC(TRUESIZE(oBM,dy,UM));
-         w = W_ALLOC(2*(n+1)); w1 = W_ALLOC(DEG(f1)); w2 = W_ALLOC(DEG(f2));
+   DEG(p) = dy;
-         for ( i = DEG(f1); i >= 0; i-- ) {
+   for ( i = 0, c = (UM *)COEF(p); i <= dy; i++ ) {
-                 for ( j = n - 1, px = p1[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- );
+     c[i] = UMALLOC(dx);
-                 w1[i] = ( j == -1 ? 0 : 1 );
+     clearum(c[i],dx);
-         }
+   }
-         for ( i = DEG(f2); i >= 0; i-- ) {
+   return p;
-                 for ( j = n - 1, px = p2[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- );
-                 w2[i] = ( j == -1 ? 0 : 1 );
-         }
-         for ( j = DEG(fr) = DEG(f1) + DEG(f2); j >= 0; j-- ) {
-                 for ( i = n - 1, px = COEF(fr)[j]; i >= 0; i-- )
-                         px[i] = 0;
-                 for ( max = MIN(DEG(f1),j), i = MAX(0,j-DEG(f2)); i <= max; i++ )
-                         if ( w1[i] != 0 && w2[j - i] != 0 ) {
-                                 mulpadic(mod,n,p1[i],p2[j - i],w); addpadic(mod,n,w,px);
-                         }
-         }
  }
- void cpylum(bound,p,r)
+ void mullum(int mod,int n,LUM f1,LUM f2,LUM fr)
- int bound;
- LUM p,r;
  {
-         register int i,j;
+   int max;
-         register int **pp,**ppr;
+   register int i,j,**p1,**p2,*px;
+   int *w,*w1,*w2;
-         DEG(r) = DEG(p);
+   p1 = (int **)COEF(f1); p2 = (int **)COEF(f2);
-         for ( i = 0, pp = COEF(p), ppr = COEF(r);
+   w = W_ALLOC(2*(n+1)); w1 = W_ALLOC(DEG(f1)); w2 = W_ALLOC(DEG(f2));
-                 i <= DEG(p); i++ )
+   for ( i = DEG(f1); i >= 0; i-- ) {
-                 for ( j = 0; j < bound; j++ )
+     for ( j = n - 1, px = p1[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- );
-                         ppr[i][j] = pp[i][j];
+     w1[i] = ( j == -1 ? 0 : 1 );
+   }
+   for ( i = DEG(f2); i >= 0; i-- ) {
+     for ( j = n - 1, px = p2[i]; ( j >= 0 ) && ( px[j] == 0 ); j-- );
+     w2[i] = ( j == -1 ? 0 : 1 );
+   }
+   for ( j = DEG(fr) = DEG(f1) + DEG(f2); j >= 0; j-- ) {
+     for ( i = n - 1, px = COEF(fr)[j]; i >= 0; i-- )
+       px[i] = 0;
+     for ( max = MIN(DEG(f1),j), i = MAX(0,j-DEG(f2)); i <= max; i++ )
+       if ( w1[i] != 0 && w2[j - i] != 0 ) {
+         mulpadic(mod,n,p1[i],p2[j - i],w); addpadic(mod,n,w,px);
+       }
+   }
  }
- void pwrlum(mod,bound,p,n,r)
+ void cpylum(int bound,LUM p,LUM r)
- int mod,bound,n;
- LUM p,r;
  {
-         LUM t,s;
+   register int i,j;
+   register int **pp,**ppr;
-         if ( n == 0 ) {
+   DEG(r) = DEG(p);
-                 DEG(r) = 0;
+   for ( i = 0, pp = COEF(p), ppr = COEF(r);
-                 COEF(r)[0][0] = 1;
+     i <= DEG(p); i++ )
-         } else if ( DEG(p) < 0 )
+     for ( j = 0; j < bound; j++ )
-                 DEG(r) = -1;
+       ppr[i][j] = pp[i][j];
-         else if ( n == 1 )
-                 cpylum(bound,p,r);
-         else {
-                 W_LUMALLOC(DEG(p)*n,bound,t);
-                 pwrlum(mod,bound,p,n/2,t);
-                 if ( !(n%2) )
-                         mullum(mod,bound,t,t,r);
-                 else {
-                         W_LUMALLOC(DEG(p)*n,bound,s);
-                         mullum(mod,bound,t,t,s);
-                         mullum(mod,bound,s,p,r);
-                 }
-         }
  }
- int **almat(n,m)
+ int isequalum(UM f1,UM f2)
- int n,m;
  {
-         int **mat,i;
+   int i;
-         mat = (int **)MALLOC(n*sizeof(int *));
+   if ( DEG(f1) < 0 )
-         for ( i = 0; i < n; i++ )
+     if ( DEG(f2) < 0 )
-                 mat[i] = (int *)CALLOC(m,sizeof(int));
+       return 1;
-         return mat;
+     else
+       return 0;
+   else if ( DEG(f2) < 0 )
+     return 0;
+   else {
+     if ( DEG(f1) != DEG(f2) )
+       return 0;
+     for ( i = 0; i <= DEG(f1); i++ )
+       if ( COEF(f1)[i] != COEF(f2)[i] )
+         break;
+     if ( i < DEG(f1) )
+       return 0;
+     else
+       return 1;
+   }
  }
- void mini(mod,f,fr)
+ void pwrlum(int mod,int bound,LUM p,int n,LUM r)
- register int mod;
- UM f,fr;
  {
-         register int i,j,**c,*ptr;
+   LUM t,s;
-         int d,dr,dm,n;
-         UM w,q;
-         n = DEG(f); c = (int **)ALLOCA(n*sizeof(int *));
+   if ( n == 0 ) {
-         for ( i = 0; i < n; i++ ) {
+     DEG(r) = 0;
-                 c[i] = (int *)ALLOCA(n*sizeof(int));
+     COEF(r)[0][0] = 1;
-                 bzero((char *)c[i],(int)(n*sizeof(int)));
+   } else if ( DEG(p) < 0 )
-         }
+     DEG(r) = -1;
-         w = W_UMALLOC( mod + n + 10 ); q = W_UMALLOC( mod + n + 10 );
+   else if ( n == 1 )
-         for ( i = 1; ( d = ( mod * i ) ) < n; i++ ) c[d][i - 1] = 1;
+     cpylum(bound,p,r);
-         DEG(w) = d;
+   else {
-         for ( j = 0; j < d; j++ )
+     W_LUMALLOC(DEG(p)*n,bound,t);
-                 COEF(w)[j] = 0;
+     pwrlum(mod,bound,p,n/2,t);
-         COEF(w)[d] = 1;
+     if ( !(n%2) )
-         for ( ; (i < n) && ((dr = divum(mod,w,f,q)) >= 0); i++ ) {
+       mullum(mod,bound,t,t,r);
-                 for ( j = dr; j >= 0; j-- )
+     else {
-                         COEF(w)[j + mod] = c[j][i - 1] = COEF(w)[j];
+       W_LUMALLOC(DEG(p)*n,bound,s);
-                 for ( j = mod - 1; j >= 0; j-- )
+       mullum(mod,bound,t,t,s);
-                         COEF(w)[j] = 0;
+       mullum(mod,bound,s,p,r);
-                 DEG(w) = dr + mod;
+     }
-         }
+   }
-         for ( i = 1; i < n; i++ )
-                 c[i][i - 1] = ( c[i][i - 1] + mod - 1 ) % mod;
-         if ( ( dm = minimain(mod,n,n - 1,c) ) != -1 )
-                 for ( i = 0, ptr = COEF(fr), ptr[0] = 0; i <= dm; i++ )
-                         ptr[i + 1] = c[0][i];
-         else
-                 COEF(fr)[0] = 1;
-         DEG(fr) = dm + 1;
  }
- int minimain(mod,n,m,c)
+ int **almat(int n,int m)
- register int mod;
- int n,m;
- register int **c;
  {
-         register int *ptr,*ci,*p;
+   int **mat,i;
-         register int i,l,a,j,b,inv;
-         int *tmp;
-         for ( j = 0; j < m; j++ ) {
+   mat = (int **)MALLOC(n*sizeof(int *));
-                 for ( i = j; (n > i) && !c[i][j]; i++ );
+   for ( i = 0; i < n; i++ )
-                 if ( i == n ) {
+     mat[i] = (int *)CALLOC(m,sizeof(int));
-                         for ( i = j, j = j - 1; j >= 0; j-- )
+   return mat;
-                                 c[0][j] = c[j][i];
-                         c[0][i] = mod - 1;
-                         return( i );
-                 }
-                 if ( i != j ) {
-                         tmp = c[i]; c[i] = c[j]; c[j] = tmp;
-                 }
-                 ptr = c[j]; inv = invm((ptr[j] + mod) % mod,mod);
-                 for ( l = j, p = ptr+l; l < m; l++ ) {
-                         a = (*p * inv) % mod;
-                         *p++ = (a<0?a+mod:a);
-                 }
-                 for ( i = 0; i < n; i++ )
-                         if ( (a = -c[i][j]) && (i != j) ) {
-                                 for ( l = j+1, p = ptr+l, ci = c[i]+l; l < m; l++ ) {
-                                         b = (*p++ * a + *ci) % mod;
-                                         *ci++ = (b<0?b+mod:b);
-                                 }
-                                 c[i][j] = 0;
-                         }
-         }
-         return (-1);
  }
- #if defined(__GNUC__) || defined(THINK_C)
+ void mini(int mod,UM f,UM fr)
+ {
+   register int i,j,**c,*ptr;
+   int d,dr,dm,n;
+   UM w,q;
+   n = DEG(f); c = (int **)ALLOCA(n*sizeof(int *));
+   for ( i = 0; i < n; i++ ) {
+     c[i] = (int *)ALLOCA(n*sizeof(int));
+     bzero((char *)c[i],(int)(n*sizeof(int)));
+   }
+   w = W_UMALLOC( mod + n + 10 ); q = W_UMALLOC( mod + n + 10 );
+   for ( i = 1; ( d = ( mod * i ) ) < n; i++ ) c[d][i - 1] = 1;
+   DEG(w) = d;
+   for ( j = 0; j < d; j++ )
+     COEF(w)[j] = 0;
+   COEF(w)[d] = 1;
+   for ( ; (i < n) && ((dr = divum(mod,w,f,q)) >= 0); i++ ) {
+     for ( j = dr; j >= 0; j-- )
+       COEF(w)[j + mod] = c[j][i - 1] = COEF(w)[j];
+     for ( j = mod - 1; j >= 0; j-- )
+       COEF(w)[j] = 0;
+     DEG(w) = dr + mod;
+   }
+   for ( i = 1; i < n; i++ )
+     c[i][i - 1] = ( c[i][i - 1] + mod - 1 ) % mod;
+   if ( ( dm = minimain(mod,n,n - 1,c) ) != -1 )
+     for ( i = 0, ptr = COEF(fr), ptr[0] = 0; i <= dm; i++ )
+       ptr[i + 1] = c[0][i];
+   else
+     COEF(fr)[0] = 1;
+   DEG(fr) = dm + 1;
+ }
+ int minimain(int mod,int n,int m,int **c)
+ {
+   register int *ptr,*ci,*p;
+   register int i,l,a,j,b,inv;
+   int *tmp;
+   for ( j = 0; j < m; j++ ) {
+     for ( i = j; (n > i) && !c[i][j]; i++ );
+     if ( i == n ) {
+       for ( i = j, j = j - 1; j >= 0; j-- )
+         c[0][j] = c[j][i];
+       c[0][i] = mod - 1;
+       return( i );
+     }
+     if ( i != j ) {
+       tmp = c[i]; c[i] = c[j]; c[j] = tmp;
+     }
+     ptr = c[j]; inv = invm((ptr[j] + mod) % mod,mod);
+     for ( l = j, p = ptr+l; l < m; l++ ) {
+       a = (*p * inv) % mod;
+       *p++ = (a<0?a+mod:a);
+     }
+     for ( i = 0; i < n; i++ )
+       if ( (a = -c[i][j]) && (i != j) ) {
+         for ( l = j+1, p = ptr+l, ci = c[i]+l; l < m; l++ ) {
+           b = (*p++ * a + *ci) % mod;
+           *ci++ = (b<0?b+mod:b);
+         }
+         c[i][j] = 0;
+       }
+   }
+   return (-1);
+ }
+ #if defined(__GNUC__)
  const
  #endif
  int sprime[] = {
 ,3,5,7,11,13,17,19,23,29,31,37,41,43,47,
 ,59,61,67,71,73,79,83,89,97,101,103,107,109,113,
 ,131,137,139,149,151,157,163,167,173,179,181,191,193,197,
 ,211,223,227,229,233,239,241,251,257,263,269,271,277,281,
 ,293,307,311,313,317,331,337,347,349,353,359,367,373,379,
 ,389,397,401,409,419,421,431,433,439,443,449,457,461,463,
 ,479,487,491,499,503,509,521,523,541,547,557,563,569,571,
 ,587,593,599,601,607,613,617,619,631,641,643,647,653,659,
 ,673,677,683,691,701,709,719,727,733,739,743,751,757,761,
 ,773,787,797,809,811,821,823,827,829,839,853,857,859,863,
 ,881,883,887,907,911,919,929,937,941,947,953,967,971,977,
 ,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,
 ,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,
 ,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,
 ,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,
 ,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,
 ,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,
 ,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,
 ,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,
 ,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,
 ,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,
 ,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,
 ,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,
 ,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,
 ,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,
 ,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,
 ,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,
 ,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,
 ,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,
 ,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,
 ,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,
 ,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,
 ,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,
 ,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,
 ,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,
 ,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,
 ,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,
 ,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,
 ,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,
 ,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,
 ,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,
 ,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,
 ,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,
 ,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,
 ,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,
 ,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,
 ,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,
 ,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,
 ,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,
 ,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,
 ,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,
 ,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,
 ,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,
 ,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,
 ,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,
 ,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,
 ,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,
 ,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,
 ,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,
 ,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,
 ,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,
 ,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,
 ,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,
 ,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,
 ,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,
 ,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,
 ,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,
 ,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,
 ,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,
 ,8269,8273,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387,
 ,8419,8423,8429,8431,8443,8447,8461,8467,8501,8513,8521,8527,8537,8539,
 ,8563,8573,8581,8597,8599,8609,8623,8627,8629,8641,8647,8663,8669,8677,
 ,8689,8693,8699,8707,8713,8719,8731,8737,8741,8747,8753,8761,8779,8783,
 ,8807,8819,8821,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923,8929,
 ,8941,8951,8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049,
 ,9067,9091,9103,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187,9199,
 ,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337,
 ,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439,
 ,9463,9467,9473,9479,9491,9497,9511,9521,9533,9539,9547,9551,9587,9601,
 ,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721,9733,
 ,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851,
 ,9859,9871,9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973,10007,
 ,10037,10039,10061,10067,10069,10079,10091,10093,10099,
 ,10111,10133,10139,10141,10151,10159,10163,10169,10177,
 ,10193,10211,10223,10243,10247,10253,10259,10267,10271,
 ,10289,10301,10303,10313,10321,10331,10333,10337,10343,
 ,10369,10391,10399,10427,10429,10433,10453,10457,10459,
 ,10477,10487,10499,10501,10513,10529,10531,10559,10567,
 ,10597,10601,10607,10613,10627,10631,10639,10651,10657,
 ,10667,10687,10691,10709,10711,10723,10729,10733,10739,
 ,10771,10781,10789,10799,10831,10837,10847,10853,10859,
 ,10867,10883,10889,10891,10903,10909,10937,10939,10949,
 ,10973,10979,10987,10993,11003,11027,11047,11057,11059,
 ,11071,11083,11087,11093,11113,11117,11119,11131,11149,
 ,11161,11171,11173,11177,11197,11213,11239,11243,11251,
 ,11261,11273,11279,11287,11299,11311,11317,11321,11329,
 ,11353,11369,11383,11393,11399,11411,11423,11437,11443,
 ,11467,11471,11483,11489,11491,11497,11503,11519,11527,
 ,11551,11579,11587,11593,11597,11617,11621,11633,11657,
 ,11681,11689,11699,11701,11717,11719,11731,11743,11777,
 ,11783,11789,11801,11807,11813,11821,11827,11831,11833,
 ,11863,11867,11887,11897,11903,11909,11923,11927,11933,
 ,11941,11953,11959,11969,11971,11981,11987,12007,12011,
 ,12041,12043,12049,12071,12073,12097,12101,12107,12109,
 ,12119,12143,12149,12157,12161,12163,12197,12203,12211,
 ,12239,12241,12251,12253,12263,12269,12277,12281,12289,
 ,12323,12329,12343,12347,12373,12377,12379,12391,12401,
 ,12413,12421,12433,12437,12451,12457,12473,12479,12487,
 ,12497,12503,12511,12517,12527,12539,12541,12547,12553,
 ,12577,12583,12589,12601,12611,12613,12619,12637,12641,
 ,12653,12659,12671,12689,12697,12703,12713,12721,12739,
 ,12757,12763,12781,12791,12799,12809,12821,12823,12829,
 ,12853,12889,12893,12899,12907,12911,12917,12919,12923,
 ,12953,12959,12967,12973,12979,12983,13001,13003,13007,
 ,13033,13037,13043,13049,13063,13093,13099,13103,13109,
 ,13127,13147,13151,13159,13163,13171,13177,13183,13187,
 ,13219,13229,13241,13249,13259,13267,13291,13297,13309,
 ,13327,13331,13337,13339,13367,13381,13397,13399,13411,
 ,13421,13441,13451,13457,13463,13469,13477,13487,13499,
 ,13523,13537,13553,13567,13577,13591,13597,13613,13619,
 ,13633,13649,13669,13679,13681,13687,13691,13693,13697,
 ,13711,13721,13723,13729,13751,13757,13759,13763,13781,
 ,13799,13807,13829,13831,13841,13859,13873,13877,13879,
 ,13901,13903,13907,13913,13921,13931,13933,13963,13967,
 ,13999,14009,14011,14029,14033,14051,14057,14071,14081,
 ,14087,14107,14143,14149,14153,14159,14173,14177,14197,
 ,14221,14243,14249,14251,14281,14293,14303,14321,14323,
 ,14341,14347,14369,14387,14389,14401,14407,14411,14419,
 ,14431,14437,14447,14449,14461,14479,14489,14503,14519,
 ,14537,14543,14549,14551,14557,14561,14563,14591,14593,
 ,14627,14629,14633,14639,14653,14657,14669,14683,14699,
 ,14717,14723,14731,14737,14741,14747,14753,14759,14767,
 ,14779,14783,14797,14813,14821,14827,14831,14843,14851,
 ,14869,14879,14887,14891,14897,14923,14929,14939,14947,
 ,14957,14969,14983,15013,15017,15031,15053,15061,15073,
 ,15083,15091,15101,15107,15121,15131,15137,15139,15149,
 ,15173,15187,15193,15199,15217,15227,15233,15241,15259,
 ,15269,15271,15277,15287,15289,15299,15307,15313,15319,
 ,15331,15349,15359,15361,15373,15377,15383,15391,15401,
 ,15427,15439,15443,15451,15461,15467,15473,15493,15497,
 ,15527,15541,15551,15559,15569,15581,15583,15601,15607,
 ,15629,15641,15643,15647,15649,15661,15667,15671,15679,
 ,15727,15731,15733,15737,15739,15749,15761,15767,15773,
 ,15791,15797,15803,15809,15817,15823,15859,15877,15881,
 ,15889,15901,15907,15913,15919,15923,15937,15959,15971,
 ,15991,16001,16007,16033,16057,16061,16063,16067,16069,
 ,16087,16091,16097,16103,16111,16127,16139,16141,16183,
 ,16189,16193,16217,16223,16229,16231,16249,16253,16267,
 ,16301,16319,16333,16339,16349,16361,16363,16369,16381,
  };
- #include "prime.h"

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