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 PYTHON):

Solution:
import heapq
def _mp():
	return map(int,raw_input().split())

n,k=_mp()
out=[]
x=n
while x>0:
	out.append(x%2)
	x=x/2
res=[]
for i in range(len(out)):
	if (out[i]==1):
		res.append(2**i)
if k>n or k<len(res):
	print 'NO'
else:
	left=k-len(res)
	l=len(res)-1
	res1=[]
	for i in res:
		res1.append(-i)
	hea=heapq.heapify(res1)
	flag=1
	while left>0:
		if len(res1)==0:
			flag=0
			break
		item=heapq.heappop(res1)
		if item==-1:
			flag=0
			break

		heapq.heappush(res1,item/2)
		heapq.heappush(res1,item/2)
		left-=1

	if flag==0:
		print 'NO'
	else:
		print 'YES'
		out=[]
		while len(res1)>0:
			item=heapq.heappop(res1)
			out.append(-item)
		out.sort()
		print ' '.join(str(x) for x in out)