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

Subtask | Points | Constraints |
---|---|---|

1 | 20 | |

2 | 25 | |

3 | 25 | No additional constraints. |

#### 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.

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