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:
i, k =map(int, input().split())
pows, c = [], 0
while i > 0:
	pows.append(i & 1)
	c, i = c+1, i >> 1
pows.reverse()
s, c, l = sum(pows), 0, len(pows)-1
while s != k:
	while c < l and pows[c] == 0: c +=1
	if c >= l or s > k:
		print("NO")
		raise SystemExit()
	pows[c], pows[c+1], s = pows[c]-1, pows[c+1]+2, s+1
print("YES")
for i,el in enumerate(pows):
	if el > 0:
		for _ in range(el): print(2**(l-i), end=" ")