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 Counter


def read_nums():
    return [int(x) for x in input().split()]


def get_powers_of_two(n):
    res = []
    while n > 0:
        i = 1
        while i*2 <= n:
            i *= 2
        res.append(i)
        n -= i
    return res


def main():
    n, num_k = read_nums()
    powers_of_two = Counter(get_powers_of_two(n))
    while sum(powers_of_two.values()) != num_k:
        if sum(powers_of_two.values()) < num_k:
            fixed = False
            for k in powers_of_two:
                if k > 1 and powers_of_two[k] > 0:
                    powers_of_two[k] -= 1
                    powers_of_two[k // 2] += 2
                    fixed = True
                    break
            if not fixed:
                print('NO')
                exit(0)
        else:
            fixed = False
            for k in powers_of_two:
                if powers_of_two[k] > 1:
                    powers_of_two[k] -= 2
                    powers_of_two[k * 2] += 1
                    fixed = True
                    break
            if not fixed:
                print('NO')
                exit(0)

    print('YES')
    nums = []
    for k, v in powers_of_two.items():
        for _ in range(v):
            nums.append(k)

    print(' '.join([str(x) for x in nums]))


if __name__ == '__main__':
    main()