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 = list(map(int, input().split()))
x = []
ones = 0
while(n):
	if(n%2==0):
		x.append(0)
	else:
		x.append(1)
		ones += 1
	n = int(n/2)
x.reverse()
n = ones
if(n>k):
	print("NO")
else:
	for i in range(len(x)):
		if(n==k):
			break
		if(x[i]!=0 and i+1<len(x)):
			if(n+x[i]<=k):
				n += x[i]
				x[i+1] += 2*x[i]
				x[i] = 0
			else:
				x[i] -= k-n
				x[i+1] += 2*(k-n)
				n = k
	if(n!=k):
		print("NO")
	else:
		print("YES")
		for i in range(0, len(x)):
			while(x[i]!=0):
				print(pow(2, len(x)-1-i), end = " ")
				x[i] -= 1