/*
   1996 ACM North Central Regional Programming Contest
   Problem F -- Pseudo-Random Numbers

   Ed Karrels, November 1996
*/

#include <stdio.h>

long *old;
long no;

long Cycle() {
   int i;
   long k = old[no];    for (i=0; i<no; i++) {
      if (k==old[i]) return no-i;
   }
   return 0;
}


int main() {
   long z, i, m, l, c=1;

   while (scanf("%ld %ld %ld %ld", &z, &i, &m, &l), z||i||m||l) {
      old = (long*)malloc(sizeof(long) * (m+1));
      no = -1;
      while (!Cycle()) {
	 old[++no] = l;
	 l = (z * l + i) % m;
      }
      free((char*)old);
      printf("Case %ld: %ld\n", c++, Cycle());
   }

   return 0;
}