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:
from math import *
n,k=[int(i) for i in input().split()]
b=bin(n)[2:]
o=b.count('1')

if o>k or k>n:
	print('NO')
	quit()

print('YES')
k-=o
#print(b)
ans=[]
for i in range(len(b)-1,-1,-1):
	#print(ans)
	if b[i]=='1':
		t=int(pow(2,len(b)-1-i))
		#ans.append(pow(2,b))
		#print(t,k)
		if k>=t-1:
			ans+=[1]*t
			k-=(t-1)
		else:
			l=ceil(len(b)-1-i-log(k+1,2))
			#print(l)
			#l=int((k-1)/2)
			#at=[t/pow(2,l)]*pow(2,l)
			k-=(pow(2,len(b)-i-1-l)-1)
			#print(k)
			#print(l,t)
			ans+=[pow(2,l)]*int(pow(2,len(b)-i-1-l)-k)+[pow(2,l-1)]*int(2*k)
			k=0
	#print(ans)
ans.sort()
for i in ans:
	print(int(i),end=' ')