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 = [int(x) for x in input().split()]

bi = bin(n)[2:]


max_bits = 100
arr = [0] * max_bits

for idx, bit in enumerate(bi):
    arr[len(bi) - idx - 1] = int(bit)

K = sum(arr)


def spread_one():
    global K
    for idx in range(1, max_bits):
        if arr[idx] > 0:
            arr[idx - 1] += 2
            arr[idx] -= 1
            K += 1
            break


if sum(1 for x in bi if x == '1') <= k and n >= k:
    print('YES')

    while K < k:
        spread_one()

    # print(arr)
    pow_2s = [2 ** idx for i, m in enumerate(arr) for idx in [i] * m]
    print(' '.join([str(x) for x in pow_2s]))
else:
    print('NO')