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 mod;
long long qpow(long long a, long long b) {
  long long res = 1;
  for (; b; b /= 2, a = a * a % mod) {
    if (b & 1) res = a * res % mod;
  }
  return res;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long a, b, p, x;
  long long cnt = 0;
  cin >> a >> b >> p >> x;
  mod = p;
  for (int i = (1); i < (p); i++) {
    long long limt = (x - i) / (p - 1);
    long long top = (b * qpow(qpow(a, i), mod - 2) - i + mod) % mod *
                    qpow(p - 1, p - 2) % mod;
    if (i + top * (p - 1) > x) continue;
    cnt += (limt - top) / p + 1;
  }
  cout << cnt << "\n";
  return 0;
}