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:
nk = input().split()
n = int(nk[0])
k = int(nk[1])

n_bin = []
n_cop = n
i = 0
while n_cop > 0:
	if n_cop % int(2 ** (i + 1)) != 0:
		n_bin.append(1)
		n_cop -= int(2 ** i)
	else:
		n_bin.append(0)
	i += 1

if k < sum(n_bin) or k > n:
	print("NO")
else:
	print("YES")
	sum_n_bin = sum(n_bin)
	while sum_n_bin < k:
		n_bin[-1] -= 1
		n_bin[-2] += 2
		sum_n_bin += 1
		if n_bin[-1] == 0:
			n_bin = n_bin[:-1]
	nums = []
	for i in range(len(n_bin)):
		for j in range(n_bin[i]):
			nums.append(int(2 ** i))
	print(' '.join(str(x) for x in nums))