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 sys, math
input = sys.stdin.readline

def getInts():
    return [int(s) for s in input().split()]

def getInt():
    return int(input())

def getStrs():
    return [s for s in input().split()]

def getStr():
    return input().strip()

def listStr():
    return list(input().strip())

import collections as col
import math

def prime_factors(n):
    factors = []
    num = 0
    while n % 2 == 0:
        num += 1
        n //= 2
    if num:
        factors.append((2,num))
    i = 3
    while n > 1 and i*i <= n:
        num = 0
        while n % i == 0:
            num += 1
            n //= i
        if num:
            factors.append((i,num))
        i += 2
    if n > 2:
        factors.append((n,1))
    return factors

def fails(num,C):
    for c in C:
        if c % num == 0:
            return False
    return True

def solve():
    #we need to know whether, amongst the C values, there are two or more pairwise coprime values whose product equals K
    N, K = getInts()
    C = set(getInts())
    K_facs = prime_factors(K)
    for k0, k1 in K_facs:
        if fails(k0**k1,C):
            return "No"
    return "Yes"
    
#for _ in range(getInt()):
print(solve())