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:
l = list()
n,k = tuple(map(int,input().split()))

num = n
ones = 0
while num > 0:
	if num % 2 == 1:
		l.append(1)
		ones += 1
	else:
		l.append(0)
	num //= 2

if k>n or k<ones:
	print("NO")
else:
	print("YES")
	m = len(l)-1
	while ones < k:
		if k-ones > l[m]:
			l[m-1] += 2*l[m]
			ones += l[m]
			l[m] = 0
		else:
			l[m-1] += 2*(k-ones)
			l[m] -= k-ones
			ones = k
		m-=1

	num = 1
	i = 0
	while i<len(l):
		for j in range(l[i]):
			print(num, end =' ')
		num *= 2
		i += 1