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;
int qp(int a, int b, int p) {
  int r = 1;
  for (; b; b >>= 1, a = a * 1ll * a % p)
    if (b & 1) r = r * 1ll * a % p;
  return r;
}
int main() {
  int a, b, p, ia, ip, i;
  long long x, y, w = 0, o, u, v;
  scanf("%d%d%d%lld", &a, &b, &p, &x),
      ia = qp(a, p - 2, p), ip = qp(p - 1, p - 2, p), y = (p - 1ll) * p,
      u = x / y, v = x % y;
  for (i = 1; i < p; ++i) {
    b = b * 1ll * ia % p,
    o = (((b - i) * 1ll * ip % p * (p - 1) + i) % y + y) % y;
    w += u + (v >= o);
  }
  printf("%lld", w);
  return 0;
}