Maximum Hamming Distance for Array Elements

Given an array of n non-negative integers where each integer is less than $2^m$, your task is to compute, for every element, the maximum Hamming distance between it and any other element in the array. The Hamming distance between two non-negative integers is defined as the number of positions where their $m$-bit binary representations (with leading zeros if necessary) differ.

Formally, for each $i$ (1 ≤ i ≤ n), compute:
$$\max_{1\leq j\leq n} \text{hamming}(a_i,a_j)$$

inputFormat

The first line contains two integers $n$ and $m$.

The second line contains $n$ non-negative integers $a_1, a_2, \dots, a_n$, each less than $2^m$.

outputFormat

Output $n$ integers separated by spaces, where the $i$-th integer is the maximum Hamming distance between $a_i$ and any element in the array (including itself).

sample

3 3
5 4 0

2 2 2