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.Scanner;

public class Main {
    private static long fastPow(long base, long index, long mod) {
        long res = 1l, tmp = base;
        while (index > 0) {
            if ((index & 1l) == 1l)
                res = res * tmp % mod;
            tmp = tmp * tmp % mod;
            index >>= 1;
        }
        return res;
    }

    private static long moduloReverse(long num, long mod) {
        return fastPow(num, mod - 2l, mod);
    }

    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        long a = input.nextLong();
        long b = input.nextLong();
        long p = input.nextLong();
        long x = input.nextLong();
        
        long arev = moduloReverse(a, p);

        long ans = 0l;
        for (long q = 0l; q < p - 1 && q <= x; ++q) {
            long k0 = ((q - b * fastPow(arev, q, p) % p) % p + p) % p;
            long tmp = (x - q) / (p - 1);
            if (k0 <= tmp)
                ans += (tmp - k0) / p + 1;
        }

        System.out.println(ans);
        input.close();
    }
}