In a tournament with $m$ teams, each team consisting of $n$ players, construct a playing schedule so that each player is paired up against all players in all teams except their own. That is, each player should play $(m-1) \cdot n$ games. 

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.

-----Input-----
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-----
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.

-----Examples-----
Sample Input 1:
3 2
Sample Output 1:
A1-B2 B1-A2 A3-B3
A2-B3 B2-A3 A1-B1
A3-B1 B3-A1 A2-B2

Sample Input 2:
2 3
Sample Output 2:
A1-B1 A2-C2 B2-C1
A1-C1 A2-B1 B2-C2
A1-B2 A2-C1 B1-C2
A1-C2 A2-B2 B1-C1

Source: kattis | Difficulty: HARD


Solutions: