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:
import math

def number_of_ones_bit_representation(n):

	count = 0
	while(n>0):
		count += (n%2)
		n = n//2

	return count

def max_pot_two_under(n):

		return 2**int(math.log(n,2))



def C():

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

	if(k > n):
		print("NO")
		return

	if(number_of_ones_bit_representation(n) > k):
		print("NO")
		return

	print("YES")

	count = 0
	power = max_pot_two_under(n)

	answer = []

	while(n>0):

		if(n-power >= k-(count+1)):
			answer.append(power)
			count += 1
			n -= power

		else: power //= 2

	answer = [str(x) for x in answer]
	print(" ".join(answer))

C()