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()))
n=bin(n)[2:]
if n.count("1")>k:
	print ("NO")
else:
	l=[]
	for i in range(len(n)):
		if n[i]=="1":
			l.append(2**(len(n)-i-1))
	l.sort(reverse=True)
	j=0
	while k-len(l)>0:
		# if l[-1]==1:
		# 	print ("NO")
		# 	exit(0)
		while j<(len(l)) and l[j]==1:
			j=j+1
		if j>=(len(l)):
			print ("NO")
			exit(0)
		l[j]=l[j]//2
		l.append(l[j])
	l.sort()
	print ("YES")
	for i in l:
		print (i,end=" ")