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 io,os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

n, k = map(int, input().split())
c = list(map(int, input().split()))

pr = []
x = k
for d in range(2, x + 1):
    if d * d > x:
        break
    if x % d == 0:
        pr.append(d)
        while x % d == 0:
            x //= d
if x > 1:
    pr.append(x)

f = {p: 0 for p in pr}
for x in c:
    for p in pr:
        e = 0
        while x % p == 0:
            x //= p
            e += 1
        f[p] = max(f[p], e)

ans = 'Yes'
for p, e in f.items():
    for j in range(e):
        if k % p == 0:
            k //= p
    if k % p == 0:
        ans = 'No'
print(ans)