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 long long inf = 1e18;
const int N = 1e6 + 3;
long long a, b, p, x;
long long mi(long long x, long long y) {
  long long ans = 1;
  while (y) {
    if (y & 1) ans = ans * x % p;
    x = x * x % p;
    y >>= 1;
  }
  return ans;
}
long long inv(long long x) { return mi(x, p - 2); }
int main() {
  cin >> a >> b >> p >> x;
  long long P = p * (p - 1), ans = 0;
  for (long long r = 0; r < p - 1; r++) {
    long long k = (r - b * inv(mi(a, r)) % p + p) % p;
    long long n = (k * (p - 1) + r) % P;
    if (!n) n = P;
    ans += x / P;
    if (x % P >= n) ans++;
  }
  cout << ans << endl;
  return 0;
}