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 cong(long long c, long long d, long long p) {
  if (d == 0) return 1;
  long long r = c;
  for (long long i = 2; i <= d; i++) {
    r = ((c * r) % p);
  }
  return r;
}
int main() {
  long long a, b, p, invA, j;
  long long x, n, pot = 1, cont = 0, ciclo;
  cin >> a >> b >> p >> x;
  invA = cong(a, p - 2, p);
  ciclo = p * (p - 1);
  for (long long i = 0; i < p - 1; i++) {
    if (i > 0) pot = (pot * invA) % p;
    j = (i - (pot * b) % p) % p;
    if (j < 0) j += p;
    n = j * (p - 1) + i;
    if (n <= x) cont += (x - n) / ciclo + 1;
  }
  cout << cont << endl;
  return 0;
}