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())
if(k>n):
	print("NO")
else:
	a=[2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912]
	count=0
	lis=[]
	#if(n%2!=0):
	#	n=n-1
	#	count+=1
	a=list(bin(n))
	b=a[2:]
	my=[]
	le=len(b)
	for i in range(le):
		temp=int(b[i])*((2**(le-i-1)))
		#print(2**(le-i-1))
		if(temp!=0):
			my.append(temp)
			count+=1
	if(k<count):
		print("NO")
	elif(k==count):
		print("YES")
		for i in range(count):
			print(my[i],end=" ")
	else:
		p=0
		while(1):
			if(my[p]!=1 and p<count):
				my[p]=my[p]//2
				my.append(my[p])
				count+=1
				if(count==k):
					break
			elif(my[p]==1 and p<count-1):
				p+=1
			else:
				break
		if(count==k):
			print("YES")
			for i in range(count):
				print(my[i],end=" ")
		else:
			print("NO")