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,u=map(int,input().split())
jj=u
k=str(bin(n))
k=k[2:]
lis=[]
for i in range(len(k)):
    if k[i]=='1':
        lis.append(2**(len(k)-i-1))
if len(lis)>u:
    print("NO")
    exit()
u=u-len(lis)
i=0
while u>0 and len(lis)>i:
   if lis[i]==1:
       i=i+1
   else:
       lis[i]=int(lis[i]/2)
       lis.append(lis[i])
       u=u-1
lis.sort()
if len(lis)==jj:
    for x in range(len(lis)):
        lis[x]=str(int(lis[x]))
    print("YES")
    print((" ").join(lis))
else:
    print("NO")