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:
#print(sum(map(int,('64 512 16384 65536 131072 262144 262144 131072 65536 32768 16384 16384').split())))
n,k=map(int,input().split())
now=2**30
nn=30
ans=[]
while now>n:
    nn-=1
    now//=2
ans.append(now)
n-=now
k-=1

if (k==0)and(n==0):
    print('YES')
    print(ans[0])
else:
   
    while n!=0:
        while now>n:
            nn-=1
            now//=2
        n-=now
        ans.append(now)
        k-=1
    
    if k<0:
        print('NO')
    else:
        ans.sort()
        nini=len(ans)-1
        dopi_ans=[]
        while k!=0:
            while ans[nini]<=1:
                dopi_ans.append(ans.pop(nini))
                nini-=1
                if nini<0:
                    break
            if nini<0:
                break
            alfa=ans.pop(nini)
            ans.append(alfa//2)
            ans.append(alfa//2)
            k-=1
            nini=len(ans)-1
            
            
        if nini<0:
            print('NO')
        else:
            print('YES')
            print(' '.join(map(str,ans+dopi_ans)))