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 a, b, p;
long long x;
inline int pow(int a, int b, int p) {
  long long ans = 1, base = a;
  while (b) {
    if (b & 1) {
      (ans *= base) %= p;
    }
    (base *= base) %= p;
    b >>= 1;
  }
  return (int)ans;
}
inline int inv(int x, int p) { return pow(x, p - 2, p); }
int main() {
  scanf("%d%d%d%I64d", &a, &b, &p, &x);
  long long ans = 0;
  for (int i = 1; i <= p - 1; i++) {
    int now = (long long)b * inv((long long)pow(a, i, p), p) % p;
    long long first = (long long)(p - 1) * ((i - now + p) % p) + i;
    if (first > x) continue;
    ans += (x - first) / ((long long)p * (p - 1)) + 1;
  }
  printf("%I64d\n", ans);
}