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 main():
    n, k = list(map(int, input().split(' ')))
    binary = list(map(int, '{0:0b}'.format(n)))
    bin_sum = sum(binary)

    if k > n or bin_sum > k:
        print("NO")
    else:
        print("YES")
        i = 0
        dif = k - bin_sum
        while dif:
            if binary[i] <= dif:
                binary[i + 1] += binary[i] * 2
                dif -= binary[i]
                binary[i] = 0
            else:
                binary[i + 1] += dif * 2
                binary[i] -= dif
                dif = 0
            i += 1
        binary = list(reversed(binary))
        print_bin(binary)


def print_bin(binary):

    out = filter(
        lambda a: a != "",
        [' '.join([str(2 ** bi) for _ in range(binary[bi])]) for bi in range(len(binary))]
    )
    print(' '.join(list(out)))


if __name__ == '__main__':
    main()