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 p, x, a, b, ni, ans;
void e_gcd(long long a, long long b, long long &x, long long &y) {
  if (b == 0) {
    x = 1;
    y = 0;
    return;
  }
  e_gcd(b, a % b, x, y);
  int tmp = x;
  x = y;
  y = tmp - (a / b) * y;
  return;
}
int main() {
  cin >> a >> b >> p >> x;
  long long i, j, s;
  e_gcd(a, p, ni, s);
  a = 1;
  for (j = 1; j <= p - 1; j++) {
    a = a * ni % p;
    i = (j - b * a % p + p) % p;
    long long n = i * (p - 1) + j;
    if (n <= x) ans += (x - n) / (p * (p - 1)) + 1;
  }
  cout << ans << endl;
  return 0;
}