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())
bn = bin(n)[2:][::-1]
mx = 0
mst = [0]*len(bn)
for i in range(len(bn)):
	if bn[i]=='1':
		mst[i] = 1
		mx += 1
mst = mst[::-1]
lmst = len(mst)
if mx <= k and n>=k:
	i = 0
	while sum(mst) != k:
		if sum(mst)-mst[i]+mst[i]*2 <= k:
			mst[i+1] += mst[i]*2
			mst[i] = 0
		else:
			ost = sum(mst[:i]+mst[i+1:])
			x = k - ost -mst[i]
			mst[i+1] += 2*x
			mst[i] -= x
		i += 1
		#print(mst)
	mst = mst[::-1]
	print("YES")
	for i in range(lmst):
		print((str(2**i)+' ')*mst[i], end='')
else:
	print("NO")