The playing schedule should be divided into rounds. A player can play at most one game per round. If a player does not play a game in a round, that player is said to have a bye in that round.
Your task is to write a program that constructs a playing schedule so that no player has a bye in more than $1$ round. In other words, the total number of rounds in the playing schedule should be no more than $(m-1) \cdot n + 1$.
The order of the rounds and games, and who is home and away in a game, does not matter.
The input consists of a single line with two integers $n$ and $m$ ($1 \le n \le 25$, $2 \le m \le 25$, $n \cdot m \le 100$), the number of players in a team and the total number of teams, respectively.
Output one line per round in the playing schedule. Each line should contain a space separated list of games. A game is in the format “<player>-<player>”. The players in the first team are denoted as $\texttt{A}1, \texttt{A}2, ..., \texttt{A}n$; the second team $\texttt{B}1, \texttt{B}2, \ldots \texttt{B}n$ and so on.
Sample Input 1 | Sample Output 1 |
---|---|
3 2 |
A1-B2 B1-A2 A3-B3 A2-B3 B2-A3 A1-B1 A3-B1 B3-A1 A2-B2 |
Sample Input 2 | Sample Output 2 |
---|---|
2 3 |
A1-B1 A2-C2 B2-C1 A1-C1 A2-B1 B2-C2 A1-B2 A2-C1 B1-C2 A1-C2 A2-B2 B1-C1 |
Sample Input 3 | Sample Output 3 |
---|---|
1 5 |
B1-E1 C1-D1 C1-A1 D1-E1 D1-B1 E1-A1 E1-C1 A1-B1 A1-D1 B1-C1 |