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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Solution {
    public static void main(String[] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        long a = Long.parseLong(st.nextToken());
        long b = Long.parseLong(st.nextToken());
        int p = Integer.parseInt(st.nextToken());
        long x = Long.parseLong(st.nextToken());
        long[] inverse = new long[p];
        inverse[p - 1] = b;
        for(int i = p - 2; i >= 0; i--){
            inverse[i] = (inverse[i + 1] * a) % p;
        }
        //System.out.println(inverse[0]);
        long result = 0;
        for(int i = 0; i < p - 1; i++){
            int start = (i - (int)inverse[i] + p) % p;
            long first = start * ((long)(p - 1)) + i;
            if(x >= first)
                result += ((x - first) / ((long)p * (p - 1)) + 1);
        }
        System.out.println(result);
    }
}