Problem: A positive integer x is called a power of two if it can be represented as x = 2^y, where y is a non-negative integer. So, the powers of two are 1, 2, 4, 8, 16, ....

You are given two positive integers n and k. Your task is to represent n as the sum of exactly k powers of two.

Input

The only line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 2 ⋅ 10^5).

Output

If it is impossible to represent n as the sum of k powers of two, print NO.

Otherwise, print YES, and then print k positive integers b_1, b_2, ..., b_k such that each of b_i is a power of two, and ∑ _{i = 1}^{k} b_i = n. If there are multiple answers, you may print any of them.

Examples

Input


9 4


Output


YES
1 2 2 4 


Input


8 1


Output


YES
8 


Input


5 1


Output


NO


Input


3 7


Output


NO

Solution (in PYTHON3):

Solution:
n,k=map(int,input().split())
s=bin(n)[2:]
s=list(s)
c=0
for i in range(len(s)):
    s[i]=int(s[i])
    if s[i]==1:
        c+=1
if c==k:
    s.reverse()
    ans=[]
    i=0
    p=1
    while i<len(s):
        while s[i]>0:
            ans.append(p)
            s[i]-=1
        i+=1
        p*=2
    print('YES')
    print(*ans)
elif c<k:
    l=len(s)
    tf=True
    ind=s.index(1)
    while c<k:
        s[ind]-=1
        if ind+1<l:
            s[ind+1]+=2
            c+=1
            if s[ind]==0:
                ind+=1
        else:
            tf=False
            break
    if tf:
        print('YES')
        s.reverse()
        ans=[]
        i=0
        p=1
        while i<len(s):
            while s[i]>0:
                ans.append(p)
                s[i]-=1
            i+=1
            p*=2
        print(*ans)

    else:
        print('NO')
else:
    print('NO')