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>
void exgcd(int a, int b, int &x, int &y) {
  if (b == 0)
    x = 1, y = 0;
  else
    exgcd(b, a % b, y, x), y -= a / b * x;
}
int main() {
  int a, b, p;
  long long x;
  scanf("%d%d%d%I64d", &a, &b, &p, &x);
  int ak = 1, x0, y;
  long long pp = (long long)p * (p - 1), ans = 0;
  for (int k = 1; k < p; k++) {
    ak = (long long)ak * a % p;
    exgcd(ak, p, x0, y);
    x0 = ((long long)x0 * b % p + p) % p;
    long long t1 = (long long)x0 * (p - 1) % pp * (p - 1) % pp;
    long long t2 = (long long)k * p % pp;
    long long t = (t1 + t2) % pp;
    ans += (x - t + pp) / pp;
  }
  printf("%I64d\n", ans);
  return 0;
}