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 Remainders_game {

	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 NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		String[] st = br.readLine().split(" ");
		long n = Long.parseLong(st[0]);
		long k = Long.parseLong(st[1]);

		st = br.readLine().split(" ");
		long[] arr = new long[(int) n];
		for (int i = 0; i < n; i++) {
			arr[i] = Integer.parseInt(st[i]);
		}

		long ans = 1;

		for (int i = 0; i < n; i++) {
			long temp = lcm(arr[i], ans);
			ans = gcd(k, temp);
		}

		if (ans == k) {
			System.out.println("YES");
		} else {
			System.out.println("NO");
		}

	}
}