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())
binn = [int(i) for i in bin(n)[2:]]
if n>=k>=binn.count(1):
	print("YES")
	b = [pow(2,i) for i,j in enumerate(binn[::-1]) if j]
	i = 0
	while len(b)<k:
		while b[i]>1 and len(b)<k:
			x = b[i]//2
			b[i]=x
			b.append(x)
		i+=1
	print(*b)
else:
	print("NO")