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:
import math


def gcd_iter(u, v):
    while v:
        u, v = v, u % v
    return u


n, k = map(int, input().split())
array = set(map(int, input().split()))

p = 1

slozh = False

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

if k % 2 == 0:
    slozh = True
else:
    for i in range(3, delit + 1, 2):
        if k % i == 0:
            slozh = True
            break

if not slozh:
    if k > max(array):
        print("NO")
        exit()

for i in array:
    p = (p // gcd_iter(p, i) * i)
    p = gcd_iter(p, k)
    if p == k:
        print("YES")
        exit()
print("NO")