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;
long long pw(long long x, long long y) {
  long long re = 1;
  for (; y; y >>= 1) {
    if (y & 1) {
      re = re * x % p;
    }
    x = x * x % p;
  }
  return re;
}
int main() {
  cin >> a >> b >> p >> x;
  long long an = 1, z = 0;
  for (int i = 0; i < p - 1; i++) {
    long long c = b * pw(an, p - 2) % p;
    long long n = (i * p + (p - 1) * (p - 1) * c) % (p * (p - 1));
    assert((n * an - b) % p == 0);
    z += (x - n + p * (p - 1)) / (p * (p - 1));
    an = an * a % p;
  }
  cout << z << endl;
}