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 PYTHON3):

Solution:
#prime factorize the k

import math



a=input().split(' ')

n=int(a[0])

k=int(a[1])

t=True

def gcd(a, b):

	if b==0: return a

	else: return gcd(b, a%b)



C=set(map(int, input().split()))

Composite=False



a=math.floor(math.sqrt(k+1))

if k%2==0: Composite=True

else:

	for i in range(3, a+1, 2):

		if k%i==0:

			Composite=True

			break

if not Composite:

	if k>max(C):print ('NO')

	else:

		A=set()

		z=True

		for i in C:

			if i in A: pass

			if i%k==0:

				z=False

				print ('YES')

				break

			else: A.add(i)

		if z: print('NO')



else:

	A=set()

	m=1

	for i in C:

		if i in A: pass

		else:

			A.add(i)

			m*=i/gcd(m,i)

			m%=k

			if m==0:

				t=False

				print('YES')

				break

	if t: print('NO')







# Made By Mostafa_Khaled