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 F(long long x, long long k) {
  long long g = 1;
  for (; k; k >>= 1, x = x * x % P)
    if (k & 1) g = g * x % P;
  return g;
}
int main() {
  scanf("%I64d%I64d%I64d%I64d", &A, &B, &P, &X);
  long long i, j, y, t = 1, Ans = 0, k, imax, ad;
  for (j = 1; j <= min(X, P - 1); j++) {
    t = t * A % P;
    y = F(t, P - 2);
    y = B * y % P;
    k = (j - y);
    if (k < 0) k = k % P + P;
    if (k <= (X - j) / (P - 1)) Ans += ((X - j) / (P - 1) - k) / P + 1;
  }
  printf("%I64d\n", Ans);
  return 0;
}