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:
from math import ceil

n, k = map(int, input().split())
v = n
if v < k:
    print('NO')
else:
    r = []
    s = 0
    d = 0
    g = False
    while v != 0:
        if d + ceil(v / 2) <= k:
            x = v - k + d
            print('YES')
            g = True
            for i in range(x):
                print(2 ** (s + 1), end=' ')
            for i in range(v - 2 * x):
                print(2 ** s, end=' ')
            v = 0
            k = 0
        else:
            s += 1
            if v % 2 == 0:
                v //= 2
            else:
                r.append(2 ** (s - 1))
                d += 1
                v -= 1
                v //= 2
    if not g:
        print('NO')
    else:
        print(*r)