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 power(long long base, long long power) {
  long long result = 1;
  while (power > 0) {
    if (power & 1) result = (result * base) % p;
    base = (base * base) % p;
    power = power / 2;
  }
  return result;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> a >> b >> p >> x;
  long long sol = 0;
  for (long long i = 1; i < p; i++) {
    long long t1 = power(a, i);
    long long y = (power(t1, p - 2) * b) % p;
    long long t2 = (i - y + p) % p * (p - 1) + i;
    if (t2 <= x) sol += (x - t2) / (p * (p - 1)) + 1;
  }
  cout << sol << endl;
}