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 queue import PriorityQueue

n, k = map(int, input().split())

pq = PriorityQueue()
n1 = n
while n1 > 0:
    p2 = n1 & - n1
    pq.put(-p2)
    n1 -= p2


if pq._qsize() > k or k > n:
    print('NO')
else:
    print('YES')
    while pq._qsize() < k:
        p2 = -pq.get()
        pq.put(-p2//2)
        pq.put(-p2//2)

    res = []
    while pq._qsize() > 0:
        res.append(pq.get())
    print(' '.join(map(lambda x: str(-x), sorted(res))))