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;
long long pow(long long r, long long s) {
  if (s == 0) return 1;
  if (s == 1) return r;
  long long y = pow(r, s / 2);
  y *= y;
  y %= p;
  if (s % 2) y = (y * r) % p;
  return y;
}
int main() {
  long long i, y, z, l = 0;
  scanf("%lld %lld %lld %lld", &a, &b, &p, &x);
  for (i = 1; i < p; i++) {
    y = (b * pow(a, p - i - 1)) % p;
    if (i == y)
      z = 0;
    else if (i < y)
      z = (p - 1) - y + i;
    else
      z = i - y;
    z *= p;
    z += y;
    if (z > x) continue;
    ans += (x - z) / (p * (p - 1)) + 1;
  }
  printf("%lld\n", ans);
  return 0;
}