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 heapq

def decompose(n):
    xs = []
    c = 1
    while n != 0:
        if n & 1: xs.append(c)
        n >>= 1
        c <<= 1
    return xs

def works(n, k):
    xs = decompose(n)
    lower = len(xs)
    upper = sum(xs)
    return lower <= k <= upper

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

if works(n, k):
    print('YES')
    xs = [-x for x in decompose(n)]
    heapq.heapify(xs)
    while len(xs) < k:
        w = heapq.heappop(xs)
        heapq.heappush(xs, w // 2)
        heapq.heappush(xs, w // 2)
    print(' '.join(sorted(str(-x) for x in xs)))
else:
    print('NO')