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 math


def sum_powers_of_two(target, powers_count):
    if powers_count > target:
        print('NO')
        return
    powers = []
    for i in range(math.ceil(math.log2(target))+1):
        if target & (2 ** i):
            powers.append(2**i)
    if len(powers) > powers_count:
        print('NO')
        return
    i = 0
    while len(powers) < powers_count:
        if powers[i] != 1:
            powers[i] //= 2
            powers.append(powers[i])
        if powers[i] == 1:
            i += 1
    print('YES')
    print(' '.join(list(map(str, powers))))


if __name__ == '__main__':
    n, k = list(map(int, input().split()))
    sum_powers_of_two(n, k)