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:
e,b=map(int,input().split())
s=[]
d=[]
a=e
while a:
    s+=[a%2]
    a=a//2
for i in range(len(s)):
    if s[i]:
        d+=[2**i]
if b>e or len(d)>b:
    print("NO")
elif e==b:
    print("YES")
    print(e*'1 ')
else:
    i=0
    while i<len(d) and len(d)!=b:
        if d[i]!=1:
            d+=[d[i]//2,d[i]//2]
            d.pop(i)
        else:
            i+=1
    print("YES")
    d.sort()
    s=''
    for i in d:
        s+=str(i)+' '
    print(s)