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:
import math
n,k=[int(i) for i in input().split()]
mn=0
x=n
while x!=0:
    mn+=x%2
    x//=2
if k>=mn and k<=n:
    print('YES')
    z=n-k
    res=[]
    while z>0:
        y=int(math.pow(2,int(math.log2(z+1))))
        res.append(y)
        z=z+1-y
    res+=(n-sum(res))*[1]
    res.reverse()
    print(' '.join([str(i) for i in res]))
#     if len(res)!=k or sum(res)!=n:print('ERROR')
#     else:print('Valid')
else:print('NO')