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;
using ll = long long;
ll mod;
int power(ll a, ll b) {
  ll res = 1;
  while (b) {
    if (b & 1) {
      res = (res * a) % mod;
    }
    a = (a * a) % mod;
    b >>= 1;
  }
  return res;
}
int modinv(ll x) { return power(x, mod - 2); }
ll a, b, x;
int main() {
  cin >> a >> b >> mod >> x;
  ll ans = 0;
  for (int i = 1; i < mod; ++i) {
    ll curr = (b * modinv(power(a, i))) % mod;
    ll start = (mod - 1) * ((i - curr + mod) % mod) + i;
    if (start > x) continue;
    ans += (x - start) / (mod * (mod - 1)) + 1;
  }
  cout << ans << "\n";
  return 0;
}