## COCI '22 Contest 5 #2 Diskurs

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Points: 12 (partial)
Time limit: 2.0s
Memory limit: 512M

Problem type You are given non-negative integers less than . For each of them, you are to find the maximum possible Hamming distance between it and some other element of the array .

The Hamming distance of two non-negative integers is defined as the number of positions in the binary representation of these numbers in which they differ (we add leading zeros if necessary).

Formally, for each , calculate: #### Input Specification

The first line contains two integers, and  .

The second line contains integers,  .

#### Output Specification

Output integers separated with spaces, where the -th integer is the maximum Hamming distance between and some other number in .

#### Constraints

1 20 2 25 #### Sample Input 1

4 4
9 12 9 11

#### Sample Output 1

2 3 2 3

#### Sample Input 2

4 4
5 7 3 9

#### Sample Output 2

2 3 2 3

#### Sample Input 3

4 4
3 4 6 10

#### Sample Output 3

3 3 2 3

#### Explanation for Sample 3

The numbers can be represented as in binary. Numbers and differ at places, same as numbers and . On the other hand, the number differs in at most places from all other numbers.