// gcc -O3 -o tryt tryt.c
#include<stdio.h>
#include<stdlib.h>
#include<string.h>

int m[1000], i, n, d, p, c;

int ceiling(int a, int b){ return (a+b-1)/b; }

int rep(int *m, int i, int n, int d, int plus){
 int y, z, lon;
 for(lon = 1; (z = ceiling(lon*n+plus, d)) <= i+1; lon++){
  for(y = i-lon; (y >= 0) && (m[y] == m[y+lon]); y--);
  if(i-y >= z) return 0;
 }
 return 1;
}

int eq(int *g, int *d, int l){
 for(; l--; ) if(g[l] != d[l]) return 0;
 return 1;
}

int ispal(int *m, int x, int y){
 for(; x < y && m[x] == m[y]; x++, y--); 
 return x >= y;
}

int pp(){
 int x, y, z, w = 1;
 if(!rep(m, i, n, d, p)) return 0;
 for(x = 0; x <= i; x++) for(y = x; y <= i && y-x < 2*c; y++) if(ispal(m, x, y)){
  for(z = 0; z < x && !eq(m+z, m+x, y-x+1); z++);
  if(z == x && ++w > c) return 0;
 }
 return 1;
}

void usage(){
 printf("./tryt c n d p\n");
 exit(0);
}

void main(int ac, char **av){
 if(ac != 5) usage();
 c = atoi(av[1]);
 n = atoi(av[2]);
 d = atoi(av[3]);
 p = atoi(av[4]);
 for(*m = i = 0; i < 1000;) if(pp()) m[++i] = 0; else{
  while(m[i] == 2) if(!(--i)) goto here;
  m[i]++;
 }
 printf("a word of length 1000 has been obtained\n");
 return;
 here: printf("backtracking finishes\n");
}