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())
Bin = [0] * 32
One = i = 0
while n > 0:
	if n % 2 == 1:
		Bin[i] = 1
		One+= 1
	i+=1
	n//= 2
if One > k:
	print('NO')
	exit()
for i in range(31, 0, -1):
	if One == k:
		break
	if Bin[i] >= 1:
		while Bin[i] != 0 and One < k:
			Bin[i] -= 1
			Bin[i - 1]+= 2
			One+= 1

if One < k:
	print('NO')
	exit()
print('YES')
res = []
for i in range(31):
	while Bin[i] > 0:
		res.append(str(1 << i))
		Bin[i]-= 1
print(" ".join(res))