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, y, ans;
int ksm(long long a, long long b) {
  long long r = 1;
  while (b) {
    if (b & 1) r = (r * a) % p;
    a = (a * a) % p;
    b >>= 1;
  }
  return r;
}
int main() {
  cin >> a >> b >> p >> x;
  for (long long j = 0; j <= p - 2; j++) {
    long long t = ksm(a, j);
    long long invt = ksm(t, p - 2);
    long long i = (j - b * invt % p + p) % p;
    long long y = i * (p - 1) + j;
    if (y > x) continue;
    ans += (x - y) / (p * p - p) + 1;
  }
  cout << ans << endl;
  return 0;
}