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:
s,k=[int(x) for x in input().split()]
bina=[]
o=0
n=s
tot2=[]
while n>0:
    l=0
    while 1:
        if 2**l>n//2:
            bina.append(2**l)
            n-=2**l
            break
        else:
            l+=1
if len(bina)>k:
    print('NO')
elif k>s:
    print('NO')
else:
    bina.sort()
    for item in range(k-len(bina)):  
        a=bina.pop()
        while 1:
            if a==1:
                a=bina.pop()
                tot2.append(1)
            else:
                break  
        bina.append(a//2)
        bina.append(a//2)
    if o==0:
        print('YES')
        bina=bina+tot2
        tot=''
        for item in bina:
            tot+=str(item)+' '
        print(tot[:-1])