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())
a=[1]
i=2
while(i<=n):
	a.append(i)
	i*=2
ans=[]
j=len(a)-1
x=n
while(x!=0):
	if(x>=a[j]):
		x-=a[j]
		ans.append(a[j])
	else:
		j-=1
mk=len(ans)
ans=ans[::-1]
c=0
if(k>=mk and k<=n):
	i=mk
	j=mk-1
	while(i<k):
		if(ans[j]>2):
			y=ans.pop()
			ans.append(y//2)
			ans.append(y//2)
			j+=1
		elif(ans[j]==2):
			y=ans.pop()
			j-=1
			c+=1
		i+=1
	print("YES")
	for i in range(c):
		print("1 1",end=" ")
	for ele in ans:
		print(ele,end=" ")
else:
	print("NO")