Problem: Today Pari and Arya are playing a game called Remainders.

Pari chooses two positive integer x and k, and tells Arya k but not x. Arya have to find the value <image>. There are n ancient numbers c1, c2, ..., cn and Pari has to tell Arya <image> if Arya wants. Given k and the ancient values, tell us if Arya has a winning strategy independent of value of x or not. Formally, is it true that Arya can understand the value <image> for any positive integer x?

Note, that <image> means the remainder of x after dividing it by y.

Input

The first line of the input contains two integers n and k (1 ≤ n, k ≤ 1 000 000) — the number of ancient integers and value k that is chosen by Pari.

The second line contains n integers c1, c2, ..., cn (1 ≤ ci ≤ 1 000 000).

Output

Print "Yes" (without quotes) if Arya has a winning strategy independent of value of x, or "No" (without quotes) otherwise.

Examples

Input

4 5
2 3 5 12


Output

Yes


Input

2 7
2 3


Output

No

Note

In the first sample, Arya can understand <image> because 5 is one of the ancient numbers.

In the second sample, Arya can't be sure what <image> is. For example 1 and 7 have the same remainders after dividing by 2 and 3, but they differ in remainders after dividing by 7.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class D {
    
    public static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a%b);
    }
    
    public static long lcm(long a, long b) {
        return a / gcd(a, b) * b;
    }
    
    public static void main(String[]args) throws IOException {
        BufferedReader x = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(x.readLine());
        int n = Integer.parseInt(st.nextToken());
        long k = Long.parseLong(st.nextToken());
        st = new StringTokenizer(x.readLine());
        long cur = 1;
        for (int i = 0; i < n; i++) {
            long c = Long.parseLong(st.nextToken());
            cur = lcm(c, cur);
            cur = gcd(cur, k);
        }
        System.out.println((cur == k) ? "Yes" : "No");
    }
}