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 a, b, p, x;
long long qpow(long long t, long long n) {
  long long ans = 1;
  t %= p;
  while (n >= 1) {
    if (n & 1) ans = ans * t % p;
    t = t * t % p;
    n >>= 1;
  }
  return ans;
}
int main() {
  scanf("%lld%lld%lld%lld", &a, &b, &p, &x);
  long long cnt = 0;
  long long P = (p - 1) * p;
  for (long long j = 1; j < p; ++j) {
    long long k = b % p * qpow(qpow(a, j), p - 2);
    long long i = (j - k % p + p) % p;
    long long now = (i * (p - 1) + j) % P;
    if (now == 0) now = P;
    cnt += x / P + ((x % P) >= now);
  }
  printf("%lld\n", cnt);
  return 0;
}