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:
#15:35

from math import floor, log

n, k = map(int, input().split())
pn = n
l = []

while n > 0:
    y = floor(log(n, 2))
    x = 2 ** y
    n -= x
    l.append(x)

if len(l) > k or k > pn:
    print('NO')

else:
    print('YES')
    j = 0

    while len(l) < k:
        if l[j] == 1:
            j += 1
            
        else:
            l[j] //= 2
            l.append(l[j])

        if l[j] == 1:
            j += 1

    for item in l:
        print(item, end = ' ')