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 power(long long x, long long y, long long m) {
  long long ans = 1;
  while (y) {
    if (y & 1) ans = (ans * x) % m;
    x = (x * x) % m;
    y /= 2;
  }
  return ans;
}
int main() {
  long long a, b, p, x;
  cin >> a >> b >> p >> x;
  long long ans = 0;
  map<long long, bool> m;
  for (long long i = 0; i < p; i++) {
    long long temp = (power(power(a, i, p), p - 2, p) * b) % p;
    long long j = ((temp - i + p) * power(p - 1, p - 2, p)) % p;
    long long d = i + j * (p - 1);
    if (m[d] == 0 && d <= x) {
      m[d] = 1;
      ans += ((x - d) / (p * (p - 1LL)) + 1LL);
    }
  }
  cout << ans << '\n';
}