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())
b = list(map(int,str(bin(n))[2:]))
nb =  sum(b)
rank = len(b)
while(nb<k and rank>1):
	if(b[len(b)-rank]==0):
		rank-=1
	else:
		b[len(b)-rank]-=1
		b[len(b)-rank+1]+=2
		nb+=1

if(nb == k):
	print("YES")
	l = []
	for i in range( len( b )):
		for j in range (b[len(b)-i-1]):
			l.append( pow(2,i))
	print(( " ".join(map(str,l))))
else:
	print("NO")