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 pow(long long a, long long i, long long p) {
  long long result = 1;
  while (i) {
    if (i & 1) result = (result * a) % p;
    a = (a * a) % p;
    i >>= 1;
  }
  return result;
}
long long inv(long long a, long long p) { return pow(a, p - 2, p); }
int main(void) {
  long long a, b, p, x;
  cin >> a >> b >> p >> x;
  long long total = 0;
  for (int i = 1; i < p; i++) {
    long long inverse = (b * (inv(pow(a, i, p), p) % p)) % p;
    long long first = (p - 1) * ((i - inverse + p) % p) + i;
    if (first <= x) total += (x - first) / (p * (p - 1)) + 1;
  }
  cout << total;
  return 0;
}