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 func():
    n, k = map(int, input().split())
    b = bin(n)[2::]
    s = b.count('1')
    # print(b, s)
    if s > k or k > n:
        print("NO")
        return None
    b = b[::-1]
    heap = [-(1 << i) for i in range(len(b)) if b[i] == '1']
    # print(heap)
    heapq.heapify(heap)
    while s < k:
        s += 1
        x = heapq.heappop(heap)
        heapq.heappush(heap, x // 2)
        heapq.heappush(heap, x // 2)

    print("YES")
    print(' '.join(map(lambda x: str(-x), heap)))


func()