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:
import math
n,k=map(int,input().split())
nn=n
kk=k
g=n-(k-1)
if g<=0:
    print("NO")
else:
    l=int(math.log(g,2))
    c=2**l
    li=list()
    while n>0 and k>0:
        if c+k-1<=n:
            li.append(c)
            k-=1
            n-=c
        else:
            g=n-(k-1)
            if g<=0:
                print("NO")
                exit(0)
            l=int(math.log(g,2))
            c=2**l
    if sum(li)!=nn:
        print("NO")
        exit(0)
    print("YES")
    for i in li:
        print(i,end=' ')