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:

def init_split(n):

    ind = 1
    mask = ~0
    res = []
    while n != 0:
        if (n & ind) != 0:
            res.append((n & ind))
        ind <<= 1
        mask <<= 1
        n &= mask
    return res


def split(n, k):
    init = list(reversed(init_split(n)))
    if len(init) > k:
        return []

    offset = k - len(init)
    while offset != 0:
        if init[0] == 1:
            return []
        elif init[0] < offset + 1:
            init.extend([1]*init[0])
            offset -= (init[0] - 1)
            del init[0]
        else:
            init[:1] = [int(init[0] / 2)] * 2
            offset -= 1

    return init


if __name__ == '__main__':
    n, k = map(int, input().split())
    res = split(n, k)
    if not res:
        print("NO")
    else:
        print("YES")
        print(" ".join(map(str, res)))