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 output_successful_answer(count):
    print('YES')
    power = 1
    for i in range(len(count) - 1, -1, -1):
        while count[i] > 0:
            print(power, end=' ')
            count[i] -= 1
        power *= 2
    print()

def get_ans(count, total_powers, k, i):
    while total_powers < k and i + 1 < len(count):
        if count[i] >= 1:
            count[i + 1] += 2
            count[i] -= 1
            total_powers += 1
            while total_powers < k and count[i] >= 1:
                count[i + 1] += 2
                count[i] -= 1
                total_powers += 1
        i += 1
    return total_powers

n, k = map(int, input().split())
count = list(map(int, list(bin(n)[2:])))

total_powers = get_ans(count, sum(count), k, 0)

if total_powers == k:
    output_successful_answer(count)

else:
    print('NO')