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 PYTHON):

Solution:
n, k = map(int, raw_input().strip().split())
nn = n
arr = []
while n != 0:
	arr.append(n % 2)
	n = n / 2

# arr = arr[::-1]
def solve2(arr, k, n):
	numOnes = arr.count(1)
	if k < numOnes:
		return []
	elif k > n:
		return []
	else:
		ans = []
		start = 1
		for i in xrange(len(arr)):
			if arr[i] == 1:
				ans.append(start)
				k -= 1
			start *= 2

		ones = []
		while len(ans) > 0:
			if k == 0:
				break
			k -= 1
			num = ans.pop()
			if num == 2:
				ones.append(1)
				ones.append(1)
			else:
				ans.append(num / 2)
				ans.append(num / 2)
		if k > 0:
			return []
		else:
			return ones + ans


def solve(arr, k, nn):
	if k == 1:
		if arr.count(1) == 1:
			# print "YES"
			return [nn]
		else:
			# print "NO"
			return []
	else:
		if nn == 1:
			# print "NO"
			return []
		else:
			if arr.count(1) > k:
				# print "NO"
				return []
			else:
				# print "YES"
				if arr[0] == 1:
					arr[0] = 0
					rest = solve(arr, k - 1, nn - 1)

					if rest == []:
						return []
					else:
						return [1] + rest
				else:
					ans = []
					start = 1
					for i in xrange(len(arr)):
						if arr[i] == 1:
							ans.append(start)
							k -= 1
						start *= 2

					if k == 0:
						return ans
					else:

						make = ans.pop()
						k += 1

						anss = []
						makee = make
						while make != 0:
							anss.append(make % 2)
							make /= 2
						print anss, k, make
						# ans2 = solve(anss, k, makee)
						# if ans2 == []:
						# 	return []
						# else:
						# 	return ans + ans2
					# return [nn]

ans = solve2(arr, k, nn)
ans.sort()
if ans == []:
	print "NO"
else:
	print "YES"
	print " ".join(map(str, ans))