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())
a = bin(n)[2:]
c=0
l = []
for i in range(len(a)):
    if(a[i]=='1'):
        c+=1
        l.append(pow(2,len(a)-i-1))
if(c==k):
    print("YES")
    s=""
    for i in l:
        s+=str(i)+" "
    print(s)
elif(c<k):
    i=0
    while(c!=k and i<len(l)):
        a = l[i]//2
        if(a!=0):
            l[i]=a
            l.insert(i,a)
            c+=1
        else:
            i+=1
    if(c==k):
        print("YES")
        s=""
        for i in l:
            s+=str(i)+" "
        print(s)
    else:
        print("NO")
else:
    print("NO")