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;
const long long MAX_N = 1000 * 1000 + 24;
long long a, b, p, x, ans;
long long pw(int x, int y, int mod) {
  if (y == 0) return 1;
  long long t = pw(x, y / 2, mod);
  t = 1LL * t * t % mod;
  if (y & 1) t = 1LL * t * x % mod;
  return t;
}
int main() {
  cin.tie(0), cout.tie(0), ios_base::sync_with_stdio(false);
  cin >> a >> b >> p >> x;
  for (int i = 0; i < p - 1; i++) {
    long long t = pw(a, i, p), q = (1LL * pw(t, p - 2, p) * b) % p, r;
    if (i <= x) {
      r = (x - i) / (p - 1);
      if (r >= (i - q + p) % (p)) {
        r -= (i - q + p) % (p);
        r /= p;
        r++;
        ans += r;
      }
    }
  }
  cout << ans << endl;
}