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;
inline long long read() {
  long long x = 0, f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
  return x * f;
}
long long inv[1001001], a, b, p, x, tmp = 1, ans;
int main() {
  a = read(), b = read(), p = read(), x = read(), inv[1] = 1;
  for (long long i = 2; i < p; i++) inv[i] = (p - p / i) * inv[p % i] % p;
  for (long long i = 0; i < p - 1; i++, (tmp *= a) %= p)
    ans += (x - ((i + p - b * inv[tmp] % p) % p * (p - 1) + i) + p * (p - 1)) /
           p / (p - 1);
  printf("%I64d", ans);
}