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;
int a, b, p;
long long x;
int mult(int a, int b) { return (1LL * a * b) % p; }
int pw(int a, int b) {
  int ans = 1;
  while (b > 0) {
    if (b & 1) ans = mult(ans, a);
    a = mult(a, a);
    b /= 2;
  }
  return ans;
}
int main() {
  cin >> a >> b >> p >> x;
  long long cnt = 0;
  for (int i = 1; i <= (p - 1); i++) {
    int n = mult(b, pw(pw(a, i), p - 2));
    long long q = (1LL * i * p - (1LL * n * (p - 1)));
    if (q < 0) q += (1LL * p * (p - 1));
    if (q % (1LL * p * (p - 1)) > x % (1LL * p * (p - 1)))
      cnt += (x / (1LL * p * (p - 1)));
    else
      cnt += (x / (1LL * p * (p - 1))) + 1;
  }
  cout << cnt;
  return 0;
}