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:
#!/usr/bin/env python
# coding: utf-8

# In[11]:


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


# In[12]:


oldn=n


# In[13]:


klist=[1]*k


# In[14]:


n-=k


# In[ ]:





# In[15]:


i=0
while n>0 and i<k:
    while n>=klist[i]:
        n-=klist[i]
        klist[i]=2*klist[i]
        
    i+=1


# In[16]:


if sum(klist)==oldn:
    print('YES')
    print(*klist)

else:
    print('NO')
# In[ ]: