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 int maxn = 1e5, mod = 1e9 + 7;
long long a, b, p, x, t, ans;
long long power(long long a, long long b) {
  long long ret = 1;
  for (; b; b >>= 1, a = a * a % p)
    if (b & 1) ret = ret * a % p;
  return (ret);
}
int main() {
  cin >> a >> b >> p >> x;
  for (int i = 0; i < p - 1; i++) {
    t = power(a, i);
    t = (b * (power(t, p - 2))) % p;
    t = ((t - i + p) % p * (power(p - 1, p - 2))) % p;
    if (x >= ((t * (p - 1) + i))) {
      ans += (x - (t * (p - 1) + i)) / (p * p - p) + 1;
    }
  }
  cout << ans << endl;
  return 0;
}