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 collections

n, k = map(int, input().split())

powers = []

ones = 0

if 1&n:
    ones += 1

i = 2
while i<=n:
    if i&n:
        powers.append(i)
    i*=2

if k < (len(powers) + ones):
    print('NO')
else:
    while (len(powers) > 0) and (k > (len(powers) + ones)):
        element = powers[-1]
        if element == 2:
            ones += 2
            del powers[-1]
        else:
            powers[-1] = (powers[-1]//2)
            powers.append(powers[-1])

    ans = ''
    for i in powers:
        ans += (str(i) + ' ')
    for i in range(ones):
        ans += ('1 ')
    if (k == (len(powers) + ones)):
        print('YES')
        print(ans)
    else:
        print('NO')