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 E {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int a = sc.nextInt(), b = sc.nextInt(), p = sc.nextInt();
		long x = sc.nextLong();
		
		long arr[] = new long[p];
		arr[p-1] = 1;
		for(int i=p-2;i>=0;i--){
			arr[i] = arr[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 * arr[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);
		
	}

}