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,sys
from typing import List

#calcula la descomposicion en primos de un numero n
def PrimesDiv(n):
    primes_list=[]
    cant=0
    while n%2==0:
        cant+=1
        n=n/2
    if cant:primes_list.append([2,cant])

    for i in range(3,int(math.sqrt(n))+1,2):
        cant=0
        while n%i==0:
            cant+=1
            n=n/i
        if cant:primes_list.append([i,cant])

    if n>2:primes_list.append([n,1])
    return primes_list

#Check si alnguno de los ci divide a alguno de los divisores
#de k d la forma primo^cant multiplos del primo que dividen a k
def IsContain(num,list):
    for element in list:
        if element%num==0:
            return True
    return False        

#busca el producto de primos que generan a k y llama a IsContained que busca por cada ci si 
# alguno de ellos divide a cada una d la maxima potencia de esos primos tal que divide a k
def Answer(k,input_list):
    primes_list=PrimesDiv(k)
    for prime,count in primes_list:
        bool=IsContain(prime**count,input_list)
        if not bool: return False
    return True    
    
#Recibe las entradas, llama al metodo Answer que retorna el booleno de si k/ mcm(c1,..cn)
# y en dependencia a eso retorna la respuesta     
def RemaindersGame():
    #recibiendo las entradas
    _,k= sys.stdin.readline().split()
    k=int(k)
    a=sys.stdin.readline().split()
    anciest=[]

    for x in a:
        anciest.append(int(x))
    
    #llama al metodo an
    bool=Answer(k,anciest)
    if bool:
        print("Yes")
    else:
        print("No")

RemaindersGame()