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

n, k = list(map(int, input().split()))
binnum = bin(n)[2:]
bits = [int(item) for item in binnum]

if sum(bits) > k or k > n:
    print('NO')
else:
    v, m = sum(bits), len(bits)
    ok = False
    for i in range(m):
        if k == v:
            ok = True
            break
        count = bits[i]
        if i < m - 1:
            if count >= k - v:
                bits[i + 1] +=  2 * (k - v)
                bits[i] -= (k - v)
                ok = True
                break
            else:
                bits[i+1] += 2 * bits[i]
                v += bits[i]
                bits[i] = 0
    if ok:
        print('YES')
        res = []
        for i in range(m):
            for j in range(bits[i]):
                res.append(int(math.pow(2, m - i - 1)))
        print(' '.join(map(str, res)))
    else:
        print('NO')