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 collections 
ans = collections.deque()

inp= map(int,input().split())

n,k= inp 

power = [1
         ]
p=1 
for i in range(30):
    p=p*2
    power.append(p)
x=n

    
for i in range(30,-1,-1):
    if n>=power[i]:
        n-=power[i]
        ans.append(i) 
#print(ans)
l=len(ans)
if k<l or k>x:
    
    print("NO")
  

else:
    while(l<k):
        x=ans.popleft()
    #    print(x)
        if x!=0:
            ans.append(x-1)
            ans.append(x-1)
            l+=1
        else:
            ans.append(x)
#    print(ans)
    for i in range(len(ans)):
        ans[i]=1<<ans[i]
    print("YES")
    print(*ans)