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 ans, a, b, c[1000100], x, p;
int main() {
  cin >> a >> b >> p >> x;
  c[0] = 1;
  for (int i = 1; i < p; i++) {
    c[i] = (c[i - 1] * a) % p;
    if (c[i] < 0) c[i] += p;
  }
  if (p == 2)
    cout << (x + 1) / 2 << endl;
  else {
    for (int i = 1; i < p; i++) {
      long long tmp = (i * p + c[p - 1 - i] * b * (1 - p)) % (p * (p - 1));
      if (tmp < 0) tmp += p * (p - 1);
      if (tmp > 0 && tmp <= x) ans++;
      long long lol = (x - tmp) / (p * (p - 1));
      if (lol > 0) ans += lol;
    }
    cout << ans << endl;
  }
}