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.StringTokenizer;

public class Main {
    void solve() {
        int n = ni();
        int k = ni();
        int N = 1000001;
        int[] gpd = new int[N];
        for (int i = 2; i < N; i++) {
            if (gpd[i] == 0) {
                for (int j = i; j < N; j += i) {
                    gpd[j] = i;
                }
            }
        }
        int[] maxPower = new int[N];
        for (int i = 0; i < n; i++) {
            int c = ni();
            while (c > 1) {
                int cnt = 0;
                int curD = gpd[c];
                while (c % curD == 0) {
                    cnt++;
                    c /= curD;
                }
                maxPower[curD] = Math.max(maxPower[curD], cnt);
            }
        }
        while (k > 1) {
            int cnt = 0;
            int curD = gpd[k];
            while (k % curD == 0) {
                cnt++;
                k /= curD;
            }
            if (maxPower[curD] < cnt) {
                write("No");
                return;
            }
        }
        write("Yes");
    }

    int getMask(int n) {
        int mask = 1;
        while (mask <= n) {
            mask = mask << 1;
        }
        mask -= 1;
        return mask;
    }


    public static void main(String[] args){
        Main m = new Main();
        m.solve();
        try {
            m.writer.close();
        } catch (IOException e) {};
    }
    BufferedReader reader;
    BufferedWriter writer;
    StringTokenizer tokenizer;
    public Main() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        writer = new BufferedWriter(new OutputStreamWriter(System.out));
    }
    int ni() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {}
        }
        return Integer.parseInt(tokenizer.nextToken());
    }
    String nl() {
        try {
            return reader.readLine();
        } catch(IOException e) {};
        return "";
    }
    void write(String s) {
        try {
            writer.write(s);
        } catch(IOException e) {};
    }
}