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 heapq import *

def main():
	# print(max(3, 4))
	n, k = map(int, input().split())
	if k > n:
		print('NO')
		return
	l = n.bit_length()
	require = [0] * l
	for i in range(l):
		if n & (1 << i):
			require[i] = 1
			k -= 1
			if k < 0:
				print('NO')
				return
	print('YES')
	for i in range(l):
		if require[i]:
			require[i] += min((1 << i) - 1, k)
			k -= min((1 << i) - 1, k)
			if not k:
				break
	# print(require)
	for i in range(l):
		if require[i]:
			t = [(-1) * (1 << i)]
			require[i] -= 1
			while require[i]:
				a = heappop(t)
				a = -a
				heappush(t, -(a // 2))
				heappush(t, -(a // 2))
				require[i] -= 1
			print(' '.join(map(lambda x: str(-x), t)), end=' ')




if __name__ == '__main__':
	main()