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:
import sys
a,K=map(int,raw_input().split())
k=0
ans=True
dic={1:0}
potencias=[1]
passado=1
for i in xrange(30):
	dic[passado*2]=0
	passado*=2
	potencias.append(passado)
potencias1=potencias[::-1]
for i in potencias1:
	if a>=i:
		dic[i]+=a/i
		k+=a/i
		a=a%i
while k<K and ans:
	flag=False
	for i in dic:
		if dic[i]>=1 and i>1:
			dic[i]-=1
			dic[i/2]+=2
			k+=1
			flag=True
			break
	if not flag:
		ans=False
		break	
		
	
if k!=K:
	print 'NO'
else:
	print 'YES'
	for i in dic:
		for j in xrange(dic[i]):
			sys.stdout.write(str(i)+" ")