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 x, a, b, p, ans;
long long fastpower(long long base, long long power, long long m) {
  long long result = 1;
  while (power) {
    if (power & 1) result = result * base % m;
    power >>= 1;
    base = (base * base) % m;
  }
  return result % m;
}
int main() {
  long long c, k, minn;
  scanf("%lld%lld%lld%lld", &a, &b, &p, &x);
  long long temp = a;
  for (long long i = 1; i < p; i++, temp = (temp * a) % p) {
    c = (b * fastpower(temp, p - 2, p)) % p;
    k = (i - c + p) % p;
    minn = i + k * (p - 1);
    if (x >= minn) ans += (x - minn) / (p * (p - 1)) + 1;
  }
  printf("%lld", ans);
}