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())
s = bin(n).replace("0b","")
if s.count('1') > k:
    print("NO")
elif n < k:
    print("NO")
else:
    print("YES")
    ans = []
    s=s[::-1]
    if s[0]=='1':
        ans.append(1)
        k-=1 
    aux = deque()
    #print(s)
    for i in range(1,len(s)):
        if s[i]=='1':
            aux.append(2**i)
    #print(aux)
    while len(aux) < k:
        p = aux.pop()
        a,b = p//2, p//2
        if a==1:
            k-=2
            ans.extend([1,1])
        else:
            aux.appendleft(a)
            aux.appendleft(b)
    ans+=aux
    ans.sort()
    print(*ans)