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 = []
while n > 0:
	i = 1
	while i * 2 <= n:
		i *= 2
	n -= i
	a.append(i)

if len(a) > k:
	print('NO')
	exit()

k -= len(a)
i = 0
while k > 0 and i < len(a):
	while a[i] > 1 and k > 0:
		a.append(a[i] // 2)
		a[i] = a[i] // 2
		k -= 1
	i += 1

if k == 0:
	print('YES')
	for i in a[:-1]:
		print(i, end=' ')
	print(a[-1])
else:
	print('NO')