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 quick_pw(ll a, ll b, ll m) {
  ll ans = 1, base = a % m;
  for (int i = 0; i < 30; i++) {
    if (b & (1 << i)) ans = (ans * base) % m;
    base = (base * base) % m;
  }
  return ans;
}
ll rev(ll a, ll p) { return quick_pw(a, p - 2, p); }
int main() {
  ll a, b, p, x, ans = 0;
  cin >> a >> b >> p >> x;
  for (ll i = 1; i < p; i++) {
    ll cur_mult = (b * rev(quick_pw(a, i, p), p)) % p;
    ll first_meet = (p - 1) * ((i - cur_mult + p) % p) + i;
    if (x < first_meet)
      continue;
    else
      ans += (x - first_meet) / (p * (p - 1)) + 1;
  }
  cout << ans;
  return 0;
}