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:
x,y=map(int,input().split())
a=0 #bits
b=0 #powers
ind=0
s=[]
while x>0:
	if x%2==1:
		a+=1
		b+=(1<<ind)
		s.append(1<<ind)
	x>>=1
	ind+=1

if y<a or y>b:
	print('NO')
	exit(0)

if x==y:
	print('YES')
	for n in range(x):
		print(1,end=' ')
		exit(0)
 
s.reverse()
n=0
res=[]
while s[n]<y:
	y-=s[n]
	res+=[1]*s[n]
	n+=1
res+=s[n+1:]
y-=len(s)-(n+1)
cnt=[0,s[n]]
k=1
dgt=1
while dgt<y:
	cnt.append(cnt[k]//2)
	cnt.append(cnt[k]//2)
	k+=1
	dgt+=1
	if dgt==y:
		break
	cnt.append(cnt[k]//2)
	cnt.append(cnt[k]//2)
	k+=1
	dgt+=1
cnt.reverse()
for n in range(y):
	res.append(cnt[n])
print('YES')
print(*res)