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, ans;
int get(int x, int t) {
  if (t == 0) return 1;
  long long tmp = get(x, t / 2);
  tmp = tmp * tmp % p;
  if (t & 1) tmp = tmp * x % p;
  return tmp;
}
int main() {
  scanf("%I64d%I64d%I64d%I64d", &a, &b, &p, &x);
  for (int j = 1; j <= p - 1; j++) {
    int tmp = b * get(get(a, j), p - 2) % p;
    long long fir = (p - 1) * ((j - tmp + p) % p) + j;
    if (fir > x) continue;
    ans += (x - fir) / (p * (p - 1)) + 1;
  }
  printf("%I64d\n", ans);
}