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, ok, ans;
long long Pow(long long x, long long n) {
  if (n == 0) return 1;
  if (n == 1) return x;
  long long tmp = Pow(x, n / 2);
  tmp = (tmp * tmp) % p;
  if (n % 2) tmp = (tmp * x) % p;
  return tmp;
}
int main() {
  cin >> a >> b >> p >> x;
  long long ans = 0;
  long long mod = p * (p - 1);
  for (long long i = 1; i < p; ++i) {
    long long tmp = Pow(a, i);
    tmp = (Pow(tmp, p - 2) * b) % p;
    ok = (p * i + ((p - 1) * (p - 1) % mod) * tmp) % mod;
    ans = (ans + x / mod + (x % mod >= ok));
  }
  cout << ans;
  return 0;
}