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, Mod, x, ans;
long long qpow(long long x, long long y) {
  long long res = 1;
  while (y) {
    if (y & 1) res = res * x % Mod;
    x = x * x % Mod;
    y >>= 1;
  }
  return res;
}
int main() {
  cin >> a >> b >> Mod >> x;
  long long inv = qpow(a, Mod - 2);
  long long y = b;
  for (long long j = 1; j <= Mod - 1; j++) {
    y = y * inv % Mod;
    long long i = (j - y + Mod) % Mod;
    long long n = (Mod - 1) * i + j;
    if (n > x) continue;
    ans += (x - n) / ((long long)(Mod - 1) * Mod) + 1;
  }
  cout << ans;
}