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>
long long a, b, p, x;
long long FP(long long x, int k) {
  long long t = 1;
  for (; k; k >>= 1, x = x * x % p)
    if (k & 1) t = t * x % p;
  return t;
}
long long inv(long long x) { return FP(x, p - 2); }
int main() {
  scanf("%I64d%I64d%I64d%I64d", &a, &b, &p, &x);
  long long res = 0, P = p * (p - 1);
  for (int y = 1; y < p; ++y) {
    long long k = (y - b * inv(FP(a, y)) % p + p) % p;
    long long n = (p - 1) * k + y;
    if (n <= x) res += (x - n) / P + 1;
  }
  printf("%I64d", res);
  return 0;
}