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())
L=[]
L2=[]
i=1
n2=n
while i<=n:
    L2.append(i)
    i*=2
while n!=0:
    x=L2[len(L2)-1]
    while x<=n:
        n-=x
        L.append(x)
    L2=L2[:len(L2)-1]
if len(L)>k or n2<k:
    print('NO')
else:
    Ljedan=[]
    L2=L[:]
    while (len(L2)+len(Ljedan))!=k:
        x=L2[len(L2)-1]
        if x%2==0:
            L2.pop()
            L2=L2+[x//2,x//2]
        else:
            L2.pop()
            Ljedan.append(1) 
    L2.sort()
    L2=Ljedan+L2
    print('YES')
    for i in range(k):
        print(L2[i],end=' ')