Problem: Given an integer x. Your task is to find out how many positive integers n (1 ≤ n ≤ x) satisfy $$$n ⋅ a^n ≡ b   (mod\;p), where a, b, p$$$ are all known constants.

Input

The only line contains four integers a,b,p,x (2 ≤ p ≤ 10^6+3, 1 ≤ a,b < p, 1 ≤ x ≤ 10^{12}). It is guaranteed that p is a prime.

Output

Print a single integer: the number of possible answers n.

Examples

Input

2 3 5 8


Output

2


Input

4 6 7 13


Output

1


Input

233 233 10007 1


Output

1

Note

In the first sample, we can see that n=2 and n=8 are possible answers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long a, b, p, x;
long long binexp(long long base, long long p, long long MOD) {
  if (p == 0) return 1LL;
  if (p == 1) return base % MOD;
  if (p % 2 == 1) return (base * binexp(base, p - 1, MOD) + MOD) % MOD;
  return binexp((base * base + MOD) % MOD, p / 2, MOD);
}
int main() {
  scanf(" %lld%lld%lld%lld", &a, &b, &p, &x);
  long long ans = 0;
  for (int i = 1; i < p; i++) {
    long long v = (b * binexp(binexp(a, i, p), p - 2, p) + p) % p;
    long long fv = (p - 1) * ((i - v + p) % p) + i;
    if (fv > x) continue;
    fv = (x - fv) / (p * (p - 1));
    ans += fv + 1;
  }
  printf("%lld\n", ans);
}