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>
long long a, b, p, x, y;
long long u;
long long inva;
long long ans;
long long power(long long r, long long s) {
  long long re = 1;
  while (s) {
    if (s & 1) re = re * r % p;
    r = r * r % p;
    s /= 2;
  }
  return re;
}
int main() {
  scanf("%I64d %I64d %I64d %I64d", &a, &b, &p, &x);
  inva = power(a, p - 2);
  ans = 0;
  for (int i = 0; i < p - 1; ++i) {
    u = (b + p - i) * (p - 1) % p;
    y = (x - i);
    if (y < 0)
      y = -1;
    else
      y = y / (p - 1);
    if (u <= y) {
      ans += (y - u) / p + 1;
    }
    b = b * inva % p;
  }
  printf("%I64d\n", ans);
  return 0;
}