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:
# -*- coding: utf-8 -*-

from collections import deque

N, K = map(int, input().split())

if N < K:
    print('NO')
    exit()

mn = 0
que = deque()
for i in range(30, -1, -1):
    num = 2 ** i
    if N >= num:
        N -= num
        mn += 1
        que.append(num)

if len(que) > K:
    print('NO')
    exit()

while len(que) != K:
    cur = que.popleft()
    cur //= 2
    if cur != 1:
        que.appendleft(cur)
        que.appendleft(cur)
    else:
        que.append(cur)
        que.append(cur)

print('YES')
print(*(sorted(que)))