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 = 1010, maxm = 1010;
int a, b, p;
long long x, ans;
int pw(int a, int b, int mo) {
  int res = 1;
  for (; b;) {
    if (b & 1) {
      res = 1LL * res * a % mo;
    }
    a = 1LL * a * a % mo;
    b >>= 1;
  }
  return res;
}
int main() {
  int i, j, y, a0;
  long long t;
  scanf("%d%d%d%I64d", &a, &b, &p, &x);
  for (i = (1); i <= (p - 1); i++) {
    y = 1LL * b * pw(pw(a, i, p), p - 2, p) % p;
    a0 = (i - y + p) % p;
    t = (x - i < 0 || (x - i) / (p - 1) - a0 < 0)
            ? 0
            : ((x - i) / (p - 1) - a0) / p + 1;
    ans += t;
  }
  printf("%I64d", ans);
  return 0;
}