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(" "))
s=[]

if n<k:
    print("NO")

else:
    while n>0:
        s.append(int(n%2))
        n=int(n/2)
    
    if k<sum(s):
        print("NO")
    
    else:
        print("YES")
        
        for i in range(len(s)):
            while s[len(s)-i-1]!=0:
                if sum(s)==k:
                    break
                s[len(s)-i-1]-=1
                s[len(s)-i-2]+=2
            else:
                continue
            break
        
        ans=[]
        for i in range(len(s)):
            while s[i]!=0:
                ans.append(2**i)
                s[i]-=1
        print(*ans)