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 PYTHON):

Solution:
from math import log,floor

n,k=map(int,raw_input().split())
ans=list()
if(n&1):
   n=n-1;
   k=k-1;
   ans.append(1);

res=n
p=list()
while res>0:
   v=int(floor(log(res)/log(2)))
   res=res-pow(2,v)
   p.append(v)

if(len(ans)==1):
  p.append(0)
  k=k+1

occ={i:0 for i in xrange(p[0]+1)}

occ[0]=0
for i in p: 
    occ[i]=occ[i]+1

m=len(p)
#print occ

s=sorted(occ.keys())
if(m>k):
  for key in s:
      while(occ[key]>1 and m>k):
        occ[key+1]+=1
        occ[key]-=2
        m-=1;
      if(m==k): break  

s.reverse()
if(m<k):
     for key in s:
         while(occ[key]>=1 and m<k and key>0):
            occ[key-1]+=2
            occ[key]-=1
            m+=1
  
if(m==k):
    print "YES"
    ans=""
    for i in occ:
        ans=ans+(str(2**i)+" ")*occ[i] 
    print ans
else:
    print "NO"