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())
c = 0
a = []
while n :
	c += n&1
	a.append(n&1)
	n >>= 1
i = len(a)-1
while i>0 and c < k:
	if a[i] >= 1:
		a[i] -= 1
		a[i-1] += 2
		c += 1
	else:
		i -= 1
if c != k:
	print "NO"
	exit()
print "YES"
p = 1
i=0
while i<len(a):
	while a[i]:
		a[i] -= 1
		print p, 
	i += 1
	p *= 2