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 a, b, p, x;
long long inv[1000005];
int main() {
  scanf("%lld%lld%lld%lld", &a, &b, &p, &x);
  inv[1] = 1;
  for (int i = 2; i < 1000005; i++) inv[i] = (p - p / i) * inv[p % i] % p;
  long long ans = 0, ret = a;
  for (long long i = 1; i < p - 1 && i <= x; i++) {
    if (ret * i % p == b) ans++;
    ret = ret * a % p;
  }
  ret = 1;
  for (long long i = 0; i < p - 1; i++) {
    long long mx = (x - i) / (p - 1);
    long long xx = ((b * inv[ret] - i + p) % p) * inv[p - 1] % p;
    ans += (mx - xx) / p + (xx > 0 && xx * (p - 1) + i <= x);
    ret = ret * a % p;
  }
  return 0 * printf("%lld\n", ans);
}