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.IOException;
import java.io.InputStreamReader;

public class D {
	public static void main(String[] args) throws IOException  {
		BufferedReader in= new BufferedReader(new InputStreamReader(System.in));
		String [] line= in.readLine().split(" ");
		int n= Integer.parseInt(line[0]);
		int k= Integer.parseInt(line[1]);
		int mod= 1;
		String [] a= in.readLine().split(" ");
		for (int i = 0; i < n; i++) {
			int anc= Integer.parseInt(a[i]);
			int b= gcd(k, anc);
			mod= lcm(mod, b);
		}
		if(mod==k){
			System.out.println("YES");
		}
		else{
			System.out.println("NO");
		}

	}
	
	public static int gcd(int a, int b){
		return b== 0 ? a: gcd(b, a%b); 
	}
	public static int lcm(int a, int b){
		return a/ gcd(a, b)*b;
	}
}