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;
int64_t pw(int64_t n, int64_t k, int64_t MOD) {
  if (k == 0) return 1;
  int64_t tmp = pw(n, k / 2, MOD);
  return k % 2 == 0 ? tmp * tmp % MOD : tmp * tmp % MOD * n % MOD;
}
int64_t inv(int64_t x, int64_t MOD) { return pw(x, MOD - 2, MOD); }
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int64_t a, b, p, x, res = 0;
  cin >> a >> b >> p >> x;
  if (a % p == 0) {
    if (b != 0)
      cout << 0;
    else
      cout << x;
  } else {
    int64_t M = 1LL * p * (p - 1);
    for (int64_t r = 0; r < p - 1; ++r) {
      int64_t a1 = r;
      int64_t a2 = inv(pw(a, r, p), p) * b % p;
      int64_t M1 = p, M2 = p - 1;
      int64_t y1 = inv(M1, p - 1), y2 = inv(M2, p);
      int64_t t = (a1 * M1 * y1 + a2 * M2 * y2) % M;
      if (x >= t) res += (x - t) / M + 1;
    }
    cout << res;
  }
}