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())
a=list(eval(i)for i in  str(bin(n))[2:])
l=a.count(1)
end=[]
if l>k:
    print('NO')
    quit()
while l<k:
    if len(a)==1:
        print('NO')
        quit()
    
    a[0]=a[0]-1
    a[1]=a[1]+2
    
    l+=1
    if a[0]==0:
        a=a[1:]
    
else:
    l=len(a)
    for i in range(l):
        for k in range(a[i]):
            end.append(str(2**(l-1-i)))
print('YES')
print(' '.join(end))