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:
from collections import deque

n_k = list(map(int, input().split()))
n, k = n_k

bin_n = bin(n)
parts = deque()
for ind, elem in enumerate(bin_n[2:]):
	if elem == "1":
		temp = ("0b1"+"0"*(len(bin_n)-ind-3))
		parts.append(int(temp, 2))
# print(*parts)

if k < len(parts) or n < k:
	print("NO")
elif k == len(parts):
	print("YES")
	print(*parts)
else:
	rem = k - len(parts)
	while rem != 0:
		part = parts.popleft()
		if part > 1:
			part = part>>1
			parts.append(part)
			parts.append(part)
			rem -= 1
		else:
			parts.append(part)
	print("YES")
	print(*parts)