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=[int(x) for x in input().split()]
binary=list(bin(N))
binary=binary[2:]
binary.reverse()
checker=[]
for i in range(len(binary)):
	if binary[i]=='1':
		checker.append(2**i)
if binary.count('1')>K or N<K:
	print("NO")
	exit()
else:
	x=0
	counter=len(checker)
	if counter==K:
		print("YES")
		print(*checker)
		exit()
	while True:
		while checker[x]%2==0:
			checker[x]=checker[x]//2
			checker.append(checker[x])
			counter+=1
			if counter==K:
				print("YES")
				print(*checker)
				exit()
		x+=1
#print(binary)
#print(checker)