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 *
n,k=map(int,input().split())
b=bin(n)[2:]
x=b.count('1')
if(b.count('1')>k):
    print('NO')
else:
    if(k>n):
        print('NO')
    else:
        ansarr=[]
        for i in range(len(b)-1,-1,-1):
            if(b[i]=='1'):
                ansarr.append(1)
            else:
                ansarr.append(0)
        diff=k-x
        i=len(b)-1
        while(i>0):
        
            if(diff>0):
                if(ansarr[i]>0):
                    if(ansarr[i]<=diff):
                        ansarr[i-1]+=(ansarr[i])*2
                        diff-=ansarr[i]
                        ansarr[i]=0
                        
                    else:
                        ansarr[i-1]+=(diff*2)
                        ansarr[i]-=diff
                        diff=0
                i-=1
            else:
                break
            #print(*ansarr,diff)
        #print(*ansarr)
        if(diff==0):
            print('YES')
            ans=[]
            for i in range(len(ansarr)):
                if(ansarr[i]>0):
                    for j in range(ansarr[i]):
                        ans.append(2**i)
            print(*ans)
        else:
            print('NO')