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,m=map(int,input().split())
k=n
d={0:n}
i=1
while (k>m) :
    c= int(d[i-1]/2)
    
    d[i-1]-=c*2
    if c==0 :
        print("NO")
        exit()
    d[i]=c
    i+=1
    k-=c
p=abs(k-m)
i-=1
while p>0 :
    if i==0 :
        print("NO")
        exit()
    v1=min(p,d[i])
    p-=v1
    d[i]-=v1
    d[i-1]+=v1*2
s=""
for x in d :
    s+=(str(2**x)+" ")*d[x]
print("YES")
print(s)