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 ll = long long;
using ld = long double;
using ull = unsigned long long;
using namespace std;
const ll N = 1e6 + 10;
ll a, b, p, res;
ll x;
ll power(ll x, ll y) {
  ll res = 1;
  while (y) {
    if (y & 1) res = res * x % p;
    x = x * x % p;
    y >>= 1;
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> a >> b >> p >> x;
  for (ll j = (0); j <= (p - 2); ++j) {
    ll y = b * power(power(a, j), p - 2) % p;
    ll lef = (p - 1) * ((j - y + p) % p) + j;
    if (lef > x) continue;
    res += (x - lef) / ((p - 1) * p) + 1;
  }
  cout << res;
  return 0;
}