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 int N = 1e6 + 9;
int64_t a, b, p, x, inv[N], cnt;
signed main() {
  cin >> a >> b >> p >> x;
  inv[1] = 1;
  for (int64_t i = 2; i < p; i++) inv[i] = (p - (p / i) * inv[p % i] % p) % p;
  for (int64_t i = 0, pow = 1; i < p - 1 && i <= x; i++, pow = pow * a % p) {
    int64_t ub = (x - i) / (p - 1), start = (p + i - b * inv[pow] % p) % p;
    if (start > ub) continue;
    int64_t temp = (ub - start) / p + 1;
    cnt += temp;
  }
  cout << cnt << '\n';
}