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 PYTHON):

Solution:
n, k = map(int, raw_input().split())
binary = list(bin(n)[2:])
ans = []
binary = [int(x) for x in binary]
tmp = binary.count(1)
i = 0
while tmp < k:
	if binary[i] == 0:
		i += 1
	if i == len(binary)-1:
		break
	binary[i+1] += 2
	binary[i] -= 1
	tmp += 1
if tmp == k:
	print "YES"
	for i in range(len(binary)):
		tmp = pow(2, len(binary) - i - 1)
		for j in range(binary[i]):
			print tmp,
else:
	print "NO"