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 tot;
long long a, b, p, x;
long long POW2(long long base, long long sup, long long MOD) {
  long long sum = 1;
  while (sup) {
    if (sup & 1) sum = sum * base % MOD;
    sup >>= 1;
    base = base * base % MOD;
  }
  return sum;
}
int main() {
  ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  cin >> a >> b >> p >> x;
  for (long long i = 1; i < p; i++) {
    long long inv = POW2(POW2(a, i, p), p - 2, p);
    long long c = b * inv % p;
    long long n = p * (p - 1);
    long long r = (p * i + (p - 1) * (p - 1) % n * c) % n;
    tot += x / n + (x % n >= r);
  }
  cout << tot << endl;
  return 0;
}