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,sys
from sys import stdin, stdout
from collections import Counter, defaultdict, deque
input = stdin.readline
I = lambda:int(input())
li = lambda:list(map(int,input().split()))

def case():
	n,p=li()
	a=bin(n)[2:]
	s=0
	for i in a:
		s+=int(i)
	if(s>p):
		print("NO")
		return 
	a=a[::-1]
	k=1
	ans=[]
	for i in range(len(a)):
		if(a[i]=='1'):
			ans.append(k)
		k*=2
	ans.sort(reverse=True)
	pink=[]
	i=0
	c=0
	while(len(ans)<p):
		if(ans[i]!=1):
			ans[i]=ans[i]//2
			ans.append(ans[i])
		else:
			c+=1
		i+=1
		if(i==len(ans)):
			if(c==len(ans)):
				print("NO")
				return 
			c=0
			i=0
		#print(ans)
	print("YES")
	print(*ans)	


			

for _ in range(1):
	case()