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, inv[1000060], l, ans;
int main() {
  scanf("%I64d%I64d%I64d%I64d", &a, &b, &p, &x);
  inv[1] = 1;
  for (int i = 2; i < p; i++) inv[i] = (p - p / i) * 1ll * inv[p % i] % p;
  long long r = 1;
  for (int i = 0; i < p - 1; i++) {
    l = i - b * inv[r] % p;
    if (l < 0) l += p;
    if (i <= x && l <= (x - i) / (p - 1)) {
      ans += ((x - i) / (p - 1) - l) / p + 1;
      if (i == 0 && l == 0) ans--;
    }
    r *= 1ll * a, r %= p;
  }
  printf("%I64d", ans);
}