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())
i=0
s=bin(n)[2:][::-1]
d={}
while pow(2,i)<=10**9:
    d[pow(2,i)]=0
    i+=1
p=-1;c=0;flag=0
for i in range(len(s)):
    if s[i]=='1':
        d[pow(2,i)]=1;c+=1
        p=i
m=0;
#print(c)
for i in d.items():
    m+=i[1]
x=d.items()
x=sorted(x,key=lambda y:y[0])
x=[list(i) for i in x]
#print (x)
while m<k:
    while p>0 and x[p][1]>0 and m<k:
        m+=1
        x[p-1][1]+=2
        x[p][1]-=1
        #print (x)
    if p==0 and m<k:
        flag=1
        break
    p-=1
if c>k:
    print ('NO')
elif flag==1:
    print ('NO')
else:
    s=""
    print('YES')
    for i in x:
        if i[1]>0:
            for _ in range(i[1]):
                print(i[0],end =' ')