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 CF687B {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		int k = Integer.parseInt(st.nextToken());
		int[] pp = new int[7];
		int[] qq = new int[7];
		int m = 0;
		for (int p = 2; p * p <= k; p++)
			if (k % p == 0) {
				int q = 0;
				while (k % p == 0) {
					k /= p;
					q++;
				}
				pp[m] = p;
				qq[m] = q;
				m++;
			}
		if (k > 1) {
			pp[m] = k;
			qq[m] = 1;
			m++;
		}
		st = new StringTokenizer(br.readLine());
		for (int i = 0; i < n; i++) {
			int c = Integer.parseInt(st.nextToken());
			for (int j = 0; j < m; j++) {
				if (qq[j] == 0)
					continue;
				int p = pp[j];
				int q = 0;
				while (c % p == 0) {
					c /= p;
					q++;
				}
				if (qq[j] <= q)
					qq[j] = 0;
			}
		}
		for (int j = 0; j < m; j++)
			if (qq[j] > 0) {
				System.out.println("No");
				return;
			}
		System.out.println("Yes");
	}
}