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:
import gc

def main():
    n, k = list(map(int, input().split()))

    if n < k:
        print('NO')
        return

    if n == k:
        print('YES')
        print(' '.join(['1', ] * k))
        return

    powers = []
    while n:
        x = 1
        while x * 2 <= n:
            x *= 2
        n -= x
        powers.append(x)

    if len(powers) > k:
        print('NO')
        return

    if len(powers) == k:
        print('YES')
        print(' '.join(list(map(str, powers))))
        return

    pd = {}
    nums = 0
    pm = max(powers)
    for e in powers:
        pd[e] = pd.get(e, 0) + 1
        nums += pd[e]

    while nums < k:
        x = pm
        while x not in pd or pd[x] == 0:
            x //= 2
        pd[x // 2] = pd.get(x // 2, 0) + 2
        pd[x] -= 1
        nums += 1

    result = []
    for k in pd:
        result.extend([k, ] * pd[k])

    print('YES')
    print(' '.join(list(map(str, result))))
    return

if __name__ == '__main__':
    gc.disable()
    main()