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 defaultdict, OrderedDict
from functools import reduce
from bisect import insort

mi = lambda: [int(i) for i in input().split()]
flat = lambda l: reduce(lambda a, b: a + b, l)


n, k = mi()
pows = [2 ** i for i in range(0, 32 + 1)]


rep = dict.fromkeys(pows, 0)

p = pows[-1]
while n:
    while pows and pows[-1] > n:
        pows.pop(-1)
    n -= pows[-1]
    rep[pows[-1]] += 1

cnt = sum(rep.values())
while cnt < k and p != 1:
    need = min(k - cnt, rep[p])
    rep[p] -= need

    p //= 2
    rep[p] += need * 2
    cnt += need

if cnt != k:
    print('NO')
else:
    print('YES')
    print(*flat([[k] * v for k, v in rep.items()]))