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 JAVA):

Solution:
import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt();
        int b = sc.nextInt();
        int p = sc.nextInt();
        long x = sc.nextLong();
        long array[] = new long[p];
        array[p - 1] = 1;
        for (int i = p - 2; i >= 0; i--) {
            array[i] = array[i + 1] * a % p;
        }
        long ans = 0;
        long T = (long) p * (p - 1);
        for (int i = 1; i <= p - 1; i++) {
            long j = (i - b * array[i]) % p;
            while (j < 0) {
                j += p;
            }
            long n = j * (p - 1) + i;
            ans += x / T;
            if (x % T >= n)
                ans++;
        }
        System.out.println(ans);
    }
}