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:
from math import log2 as log

n,k=map(int,input().split())

result=[]

if n%2==1:
    result.append(1)
    n-=1;k-=1
    #print(n,k)

while n>0 and k>0:
    temp=int(log(n))
    j=0
    
    if n>k:
        while(j<=n):
            flag=pow(2,temp-j)
            j+=1
            
            if n-flag>=k-1:
                result.append(flag)
                n-=flag;k-=1
                break
                #print(n,k)

    else:
        break


if n==k:
    print('YES')
    for i in range(len(result)):
        print(result[i],end=' ')
    for i in range(n):
        print(1,end=' ')
else:
    print('NO')