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.math.BigInteger;
import java.util.Scanner;

public class e {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int a = in.nextInt(), b = in.nextInt();
		long p = in.nextInt();
		long x = in.nextLong();
		long lcmCnts = x/(p*(p-1));
		long leftover = x % (p*(p-1));
		long miA = BigInteger.valueOf(a).modInverse(BigInteger.valueOf(p)).longValue();
		long m2 = b;
		long ans = 0;
		for(int m1=0;m1<p-1;m1++) {
			long k = m1-m2;
			long v = k*p+m2;
			long lcm = p*(p-1);
			v = ((v % lcm) + lcm) % lcm;
			ans += lcmCnts;
			if(v <= leftover)
				ans++;
			if(v == 0)
				ans--;
			m2 *= miA;
			m2 %= p;
		}
		System.out.println(ans);
	}
	
}