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:
n,k=map(int,input().split())
l=[];
while(n>=1):
    l.append(n%2);
    n=n//2;
p=[]
for i in range(len(l)):
    if(l[i]!=0):
        p.append((2**i)*l[i])
c=0
pl=len(p)
if(pl>k):
    c=-1
else:
    y=1
    cn=0
    k=k-pl
    fg=0
    while(k>0):
        if y>pl:
        	c=-1
        	break
        if p[-1]<=k:
        	cn=cn+p[-1]
        	k=k-p[-1]+1
        	p.pop(-1)
        	y+=1
        else:
        	a=-1
        	k=k+1
        	t=k
        	while(k>=1):
        		a+=1
        		k=k//2;
        	a=2**a
        	h1=(2*a)-t
        	g1=p[-1]//a
        	h2=2*(t-a)
        	g2=g1//2
        	p.pop(-1)
        	fg=1
        	break
if(c==-1):
    print("NO")
else:
    print("YES",end="\n")
    if fg==1:
    	for i in range(h1):
    		p.append(g1)
    	for i in range(h2):
    		p.append(g2)
    p.sort()
    for i in range(cn):
    	print(1,end=" ")
    for i in range(len(p)):
        print(p[i],end=" ")
    print()