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;
const int N = 1e6 + 10;
long long a, b, p, x;
long long A[N] = {1};
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cin >> a >> b >> p >> x;
  long long ans = 0;
  int i, j;
  for (i = 1; i < p; i++) A[i] = A[i - 1] * a % p;
  for (j = 1; j < p; j++) {
    long long y = b * A[p - 1 - j] % p;
    long long i = (j - y + p) % p;
    long long tmp = i * (p - 1) + j;
    if (x >= tmp) {
      ans += (x - tmp) / p / (p - 1) + 1;
    }
  }
  cout << ans << endl;
}