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;
long long pw(long long x, long long y) {
  long long res = 1;
  for (; y; y >>= 1) {
    if (y & 1) res = res * x % p;
    x = x * x % p;
  }
  return res;
}
int main() {
  scanf("%I64d %I64d %I64d %I64d", &a, &b, &p, &x);
  long long ans = 0, an = 1;
  for (int i = 0; i < p - 1; i++) {
    long long c = b * pw(an, p - 2) % p;
    long long n = (c * (p - 1) * (p - 1) + i * p) % (p * (p - 1));
    long long tmp = (x - n + p * (p - 1)) / (p * (p - 1));
    if (tmp > 0) ans = ans + tmp;
    an = an * a % p;
  }
  printf("%I64d\n", ans);
  return 0;
}