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:
n,k=map(int,input().split())
b=format(n,'b')
a=[]
for i in b:
      a.append(int(i))
l=0
if(n>=k and k>=sum(a)):
      print("YES")
      while(sum(a)!=k):
            a[l]-=1
            a[l+1]+=2
            if(a[l]==0):
                  l+=1
      x=""
      for i in range(len(a)):
            for j in range(a[i]):
                  x+=str(2**(len(a)-i-1))+" "
      print(x)
else:
      print("NO")