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())

twolist = [1]

indexStart = 0

for i in range(1, 30):
	twolist.append(twolist[-1] * 2)
	if twolist[-1] <= n:
		indexStart = i

remainSum = n
ans = []

while (remainSum > 0):
	if twolist[indexStart] <= remainSum:
		ans.append(twolist[indexStart])
		remainSum -= twolist[indexStart]
	else:
		indexStart -= 1

if len(ans) > k or k > n:
	print('NO')
else:
	rmk = len(ans)
	ir = 0
	while (ir < rmk and rmk < k):
		if (ans[ir] == 1):
			ir += 1
			continue
		
		hf = int(ans[ir] / 2)
		ans[ir] = hf
		ans.append(hf)
		rmk += 1
	
	print('YES')
	print(' '.join(map(str, ans)))