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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class D {

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(in.readLine());
        int n = Integer.parseInt(st.nextToken());
        long k = Long.parseLong(st.nextToken());
        st = new StringTokenizer(in.readLine());

        boolean yes = false;
        long cur = 1;
        for (int i = 0; i < n; i++) {
            long x = gcd(k, Long.parseLong(st.nextToken()));
            long extra = gcd(cur, x);
            x /= extra;
            cur *= x;
            if (cur == k) {
                yes = true;
                break;
            }
            // System.out.println(k);
        }

        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        out.write(yes ? "YES" : "NO");
        out.close();
    }

    private static long gcd(long K, long M) {
        long k = Math.max(K, M);
        long m = Math.min(K, M);
        while (m != 0) {
            long r = k % m;
            k = m;
            m = r;
        }
        return k;
    }
}