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 bisect import bisect_right
def main():
    res = []
    n,k = [int(i) for i in input().split()]
    if n < k:
        return []
    mult = 1
    mults = []
    while mult < 1000000001:
        mults.append(mult)
        mult *= 2
    while n > 0 and k > 0:
        i = bisect_right(mults,n) - 1
        tmp_n = n - mults[i]
        k -= 1
        if tmp_n > 0 and k == 0:
            return []
        while tmp_n < k and i >= 0:
            i -= 1
            tmp_n = n - mults[i]
        n = tmp_n
        res.append(mults[i])
    return res

res = main()
if len(res) == 0:
    print('NO')
else:
    print('YES')
    print(*res)