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,kk=map(int,input().split())
bn=str(bin(n))[2:]
if bn.count("1")>kk or n<kk:
    print("NO")
else:
    k=[0]*50
    k[0]=n
    s=n
    i=0
    while 1:
        if s<=kk:
            break
        if s-k[i]//2<kk:
            k[i+1]=s-kk
            k[i]-=(s-kk)*2
            break
        else:
            s-=k[i]//2
            k[i+1]=k[i]//2
            k[i]-=k[i]-k[i]%2
        i+=1
    print("YES")
    c=0
    for i in k:
        if i!=0:
            print((str(2**c)+" ")*i,end="")
        c+=1