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:
a, s = map(int, input().split())
d = str(bin(a))[2:]
if (a < s or s < d.count('1')): print('NO')
else:
    f = [int(d[i]) for i in range(len(d))]
    f.reverse()
    for i in range(len(f) - 1, 0, -1):
        if f[i] != 0: 
            if sum(f) + f[i] < s:
                f[i - 1] += 2 * f[i]
                f[i] = 0
            else:
                a = s - sum(f)
                f[i - 1] += a * 2
                f[i] -= a
    print('YES')
    for i in range(len(f)):
        print(f[i] * (str(2 ** i)+' '), end = '')