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 log2,ceil,floor
def check(n):
	while n!=1:
		if n%2!=0:
			return False
		n=n//2
	return True
n,k=map(int,input().split())
f=1
if k>n or (k==1 and not(check(n))):
	f=0

a=[]
t=0
p=int(log2(n))
while t<n and k>0:
	while t+2**p<=n and n-(t+2**p)>=k-1:
		a.append(2**p)
		t+=2**p
		k-=1
	p-=1
	if p<0:
		break
if t!=n:
	f=0
if f==0:
	print("NO")
else:
	print("YES")
	for i in a:
		print(i,end=" ")