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;
long long i, j, k, cnt = 0;
long long inv[1000050] = {1, 1};
long long qp(long long a, long long b, long long p) {
  long long r = 1;
  for (; b; b >>= 1, a = a * a % p)
    if (b & 1ll) r = r * a % p;
  return r;
}
int main() {
  long long a, b, p, x;
  cin >> a >> b >> p >> x;
  for (i = 2; i < p; i++) inv[i] = (p - p / i) * 1ll * inv[p % i] % p;
  long long P = (p - 1) * p, now = 1, tp = qp(p - 1, p - 2, p);
  for (i = 0; i < p - 1; i++) {
    long long y = b * (inv[now % p]) % p;
    long long r = (i * p + y * tp % p * (p - 1)) % P;
    cnt += x / P + (x % P >= r);
    now = now * a % p;
  }
  cout << cnt << endl;
  return ~~(0 ^ 0 ^ 0);
}