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 pwa[1000005], a, b, n, p, q, ans;
int main() {
  cin >> a >> b >> p >> n;
  a %= p;
  b %= p;
  q = p * (p - 1);
  ans = 0;
  pwa[0] = 1;
  for (int i = 1; i <= p; i++) pwa[i] = a * pwa[i - 1] % p;
  for (long long y = 0; y <= p - 2; y++) {
    long long x = b * pwa[p - 1 - y] % p;
    x = (y - x) % p;
    if (x < 0) x += p;
    long long c = (1 - y) - x * (p - 1), d = (n - y) - x * (p - 1),
              cc = (c < 0 || c % q == 0) ? c / q : c / q + 1,
              dd = (d > 0 || d % q == 0) ? d / q : d / q - 1;
    if (dd >= cc) ans += dd - cc + 1;
  }
  cout << ans;
  return 0;
}