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 pow_(long long i, long long j) {
  long long ii = 1;
  while (j) {
    if (j & 1) ii = (ii * i) % p;
    i = (i * i) % p;
    j >>= 1;
  }
  return ii;
}
int main() {
  scanf("%lld%lld%lld%lld", &a, &b, &p, &x);
  long long ans = 0, aj = b, inv = pow_(a, p - 2);
  for (long long j = 0; j < p - 1; ++j) {
    long long i = (j - aj + p) % p;
    if (j == 0 && i == 0) i += p;
    long long MAX = (x - j) / (p - 1);
    if (x >= j && MAX >= i) ans += MAX / p + (MAX % p >= i);
    aj = (aj * inv) % p;
  }
  printf("%lld\n", ans);
  return 0;
}