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())
if(k>n):
    print('NO')
else:
    b=bin(n)[2:]
    if(b.count('1')==k):
        b=b[::-1]
        print('YES')
        for i in range(len(b)):
            if(b[i]=='1'):
                print(1<<i,end=' ')
        print('')
        
    elif(b.count('1')<k):
        l=[]
        x=-1
        b=b[::-1]
        for i in range(len(b)):
            if(b[i]=='1'):
                l.append(1<<i)
        k-=len(l)
        for i in l:
            x+=1
            if(k<=0):
                break
            if(i!=1):
                i//=2
                k-=1
                l+=[i]*2
                l[x]=0

            
        if(k==0):
            l.sort()
            print('YES')
            for i in l:
                if(i!=0):
                    print(i,end=' ')
            print()
        else:
            print('NO')
    else:
        print('NO')