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;
const int inf = 1 << 26;
long long a, b, p, x;
long long pw(long long a, long long b, long long md) {
  long long ans = 1, base = a % md;
  while (b) {
    if (b & 1) ans = (ans * base) % md;
    base = (base * base) % md;
    b >>= 1;
  }
  return ans % md;
}
int main() {
  long long ans = 0;
  scanf("%I64d%I64d%I64d%I64d", &a, &b, &p, &x);
  for (long long i = 1; i <= p - 1; i++) {
    long long y = b * (pw(pw(a, i, p), p - 2, p)) % p;
    long long first = (p - 1) * ((i - y + p) % p) + i;
    if (first > x) continue;
    ans += (x - first) / (p * (p - 1)) + 1;
  }
  printf("%I64d\n", ans);
  return 0;
}