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:
from collections import Counter
from math import log,floor
n,k = map(int, raw_input().split())

answer = [1] * k

n -= k
i = 0
while n != 0 and i < k:
	while answer[i]<= n:
		 n -= answer[i]
		 answer[i] *= 2
	i += 1

if n != 0:
	print 'NO'
else:
	print 'YES'
	print ' '.join(map(str,answer))