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:
from math import sqrt


def factor(n):
    potentional_p = 3
    itog_list = {}
    if n % 2 == 0:
        itog_list[2] = 0
    while n % 2 == 0:
        n = n // 2
        itog_list[2] += 1
    while n - 1:
        if potentional_p > sqrt(n):
            if n in itog_list:
                itog_list[n] += 1
            else:
                itog_list[n] = 1
            return itog_list
        while n % potentional_p == 0:
            n = n // potentional_p
            if potentional_p in itog_list:
                itog_list[potentional_p] += 1
            else:
                itog_list[potentional_p] = 1
        potentional_p += 2
    return itog_list


n, k = map(int, input().split())
C = list(map(int, input().split()))
z = factor(k)
z2 = {}
for i in z:
    z2[i] = 0
for i in C:
    for d in z2:
        if z2[d] < z[d]:
            y = 0
            x = i
            while x % d == 0:
                y += 1
                x //= d
            z2[d] = max(z2[d], y)
for d in z:
    if z[d] > z2[d]:
        print('No')
        exit(0)
print('Yes')