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 $(m -1) dot.op n$ 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 $(m -1) dot.op n + 1$.
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 $m$ ($1 <= n <= 25$, $2 <= m <= 25$, $n dot.op m <= 100$), 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 "_-_". The players in the first team are denoted as $texttt(A) 1, texttt(A) 2,..., texttt(A) n$; the second team $texttt(B) 1, texttt(B) 2, \\dots texttt(B) n$ and so on.
## Input
The input consists of a single line with two integers $n$ and $m$ ($1 <= n <= 25$, $2 <= m <= 25$, $n dot.op m <= 100$), 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 "_-_". The players in the first team are denoted as $texttt(A) 1, texttt(A) 2,..., texttt(A) n$; the second team $texttt(B) 1, texttt(B) 2, \\dots texttt(B) n$ and so on.
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**Definitions**
Let $ n, m \in \mathbb{Z}^+ $ with $ 1 \leq n \leq 25 $, $ 2 \leq m \leq 25 $, $ nm \leq 100 $.
Let $ T = \{T_1, T_2, \dots, T_m\} $ be the set of $ m $ teams, where each team $ T_i $ contains $ n $ players: $ T_i = \{P_{i,1}, P_{i,2}, \dots, P_{i,n}\} $.
Let $ P = \bigcup_{i=1}^m T_i $ be the set of all players, with $ |P| = nm $.
**Constraints**
1. Each player must play exactly $ (m-1)n $ games, each against a player from a different team.
2. In each round, a player may participate in at most one game.
3. Each player may have at most one bye (i.e., no game) across the entire schedule.
4. No intra-team games are allowed.
5. Each game is an unordered pair $ \{P_{i,a}, P_{j,b}\} $ with $ i \neq j $.
**Objective**
Construct a set of rounds $ R_1, R_2, \dots, R_r $, where $ r \leq (m-1)n + 1 $, such that:
- Each round is a set of disjoint games (no player appears in more than one game per round).
- Every valid inter-team pair $ (P_{i,a}, P_{j,b}) $ with $ i \neq j $ appears in exactly one round.
- The number of players not playing in any round $ R_k $ is at most $ nm - 2 \cdot |R_k| $, and over all rounds, each player is benched at most once.