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;
int main() {
  cin >> a >> b >> p >> x;
  long long ans = 0, r = b, t, t1;
  for (int i = p - 1; i; i--) {
    if (i <= x) {
      t = (i - r + p) % p, t1 = (x - i) / (p - 1);
      ans += t1 / p + (t1 % p >= t);
    }
    r = r * a % p;
  }
  cout << ans;
}