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;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int a, b, p, x;
  cin >> a >> b >> p >> x;
  long long int ans = 0;
  long long int powe[p];
  powe[0] = 1;
  for (long long int i = 1; i < p; i++) {
    powe[i] = (powe[i - 1] * a) % p;
  }
  for (long long int j = 0; j < p - 1; j++) {
    long long int h = b * powe[p - j - 1] % p;
    long long int alph = j * p - h * (p - 1);
    double l = double(alph - x) / double(p * (p - 1));
    double r = double(alph - 1) / double(p * (p - 1));
    long long int l1 = ceil(l);
    long long int r1 = floor(r);
    ans += r1 - l1 + 1;
  }
  cout << ans << endl;
  return 0;
}