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:
from collections import deque
n,k=map(int,input().split())
f=bin(n)[2:]
t=f.count('1')
if k<t or k>n:
    print("NO")
else:
    q=deque()
    p=f[::-1]
    for i in range(len(p)):
        if(p[i]=='1'):
            q.append(pow(2,i))
    while len(q)!=k:
        o=q.pop()
        if o//2>0:
            q.append(o//2)
            q.append(o//2)
        else:
            q.appendleft(o)
    l=[]
    for i in q:
        l.append(i)
    print("YES")
    l.sort()
    print(*l)