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[1000010];
int main() {
  std::cin >> a >> b >> p >> x;
  inv[1] = 1;
  for (int i = 2; i < p; i++) inv[i] = (p - (p / i) * inv[(p % i)] % p) % p;
  long long ans = 0, apw = 1;
  for (int i = 0; i < p - 1; i++) {
    long long p1 = p - 1;
    long long z = (inv[apw] * b % p * p1 * p1 + i * p) % (p * p1);
    ans += x / (p * p1) + (x % (p * p1) >= z ? 1 : 0);
    apw = apw * a % p;
  }
  std::cout << ans << std::endl;
  return 0;
}