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 collections import deque
d=deque()
n,k=map(int,input().split())
s=bin(n)[2:]
m=s.count('1')

if(m<=k<=n):
   print('YES')
   s=s[::-1]
   for i in range(len(s)):
      if(s[i]=='1'):
         d.append(1<<i)
         
   r=k-len(d)

   while(r!=0):
      #print(d)
      x=d.pop()
      
      if(x%2==0):
         d.append(x//2)
         d.append(x//2)
         r-=1
         continue
      else:
         d.appendleft(x)
         
   
   
   print(' '.join(str(b) for b in d))
      
         

   
else:
   print('NO')