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:
#/usr/bin/env python3

import sys

a = input().split()
n = int(a[0])
k = int(a[1])

def factor(x):
	w = str(bin(x))[2:]
	return [len(w) - e[0] - 1 for e in enumerate(w) if int(e[1])]

f = factor(n)

if k < len(f):
	print("NO")
	sys.exit(0)

w = [2**x for x in f]
if sum(w) < k:
	print("NO")
	sys.exit(0)

print("YES")

while True:
	if len(w) == k:
		print(' '.join(map(str, w)))
		sys.exit(0)
	if w[0] == 2:
		w = w[1:] + [1, 1]
	elif w[0] < (k - len(w)):
		w = w[1:] + [1]*w[0]
	else:
		w = [w[0]//2, w[0]//2] + w[1:]