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:
n, k = input().split()

n = int(n)
k = int(k)

binary_array = [0] * 31


def get_min(binary, binary_array):
    minimum = 0
    for digit_idx in range(len(binary)):
        if binary[digit_idx] == '1':
            minimum += 1
            binary_array[len(binary) - digit_idx - 1] += 1
    return minimum


def reduce_element(binary_array, count, k):

    idx = len(binary_array) - 1
    while idx > 0:
        if count == k:
            break
        if binary_array[idx] > 0:
            binary_array[idx] -= 1
            binary_array[idx - 1] += 2
            count += 1
        else:
            idx -= 1


def convert(binary_array):
    answer = []
    for idx, i in enumerate(binary_array):
        if i > 0:
            array = [2**idx] * i
            if array != []:
                answer.extend(array)
    return answer

binary = format(n, 'b')
minimum = get_min(binary, binary_array)
maximum = n
if k < minimum or k > maximum:
    print("NO")
else:
    print("YES")
    count = minimum
    reduce_element(binary_array, count, k)

    answer = convert(binary_array)
    answer = [str(x) for x in answer]
    answer = ' '.join(answer)
    print(answer)