HomeAwayLeague | Topcoder Archive

Problem Statement

There are N football teams in the region. The number N is even. Each team has it own home stadium.

The league committee has decided to organize a short summer league for all N teams. The league should have the following properties:

The league will consist of exactly two rounds of football matches.
Each team will play one match in each round.
Each pair of teams will play each other at most once.
It is well known that playing at its home stadium gives the team a slight advantage. To keep the league fair, each team must play exactly one home game and one away game.

Count all valid league schedules and return that count modulo 10^9 + 7.

Formally: A match is an ordered pair (home team, away team). A round schedule is an unordered set of matches such that each team appears in exactly one match. A league schedule is an ordered pair of round schedules.

Definition

Class:: HomeAwayLeague
Method:: matches
Parameters:: int
Returns:: int
Method signature:: int matches(int x)
(be sure your method is public)

Constraints

N will be between 4 and 500,000, inclusive.
N will be even.

Examples

```
4
```
```
Returns: 12
```
Let's use (X,Y) to denote a match where X is the home team and Y is the away team, i.e., a match played at X's home stadium. Here are three of the twelve distinct valid league schedules: First round: (A,B), (C,D). Second round: (B,C), (D,A). First round: (A,B), (D,C). Second round: (B,D), (C,A). First round: (C,A), (B,D). Second round: (A,B), (D,C). Note that the third schedule can be obtained from the second one by swapping the order of the rounds. These two schedules are considered distinct.
```
8
```
```
Returns: 15120
```

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