Problem Description

You are given $n$ non-negative integers $a_1, a_2, \cdots a_n$, each of which is less than $2^m$.

For each number, you need to find its maximum Hamming distance to the other elements in the array.

The Hamming distance between two non-negative integers is defined as the number of positions where their binary representations differ (adding leading zeros if necessary).

Formally, for each $i$, compute:

$$\max\limits_{1\leq j\leq n} \operatorname{hamming}(a_i,a_j)$$

Input Format

The first line contains two integers $n$ and $m \ (1\leq n\leq 2^m,1\leq m\leq 20)$。
The second line contains $n$ numbers $a_i \ (0 \leq a_i < 2^m)$。

Output Format

Output one line with $n$ integers. The $i$-th integer represents the maximum Hamming distance between $a_i$ and the other elements in the array.

4 4
9 12 9 11

2 3 2 3

4 4
5 7 3 9

2 3 2 3

4 4
3 4 6 10

3 3 2 3

Hint

Subtask	$\text{pts}$	Constraints
$0$		Sample only
$1$	$20$	$m\leq 10$
$2$	$25$	$m\leq 16$
$3$		None

Translated by ChatGPT 5