{"raw_statement":[{"iden":"statement","content":"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.\n\nThe 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.\n\nYour 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 $(m -1) dot.op n + 1$.\n\nThe order of the rounds and games, and who is home and away in a game, does not matter.\n\nThe 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.\n\nOutput 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.\n\n"},{"iden":"input","content":"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."},{"iden":"output","content":"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."},{"iden":"examples","content":"Input3 2OutputA1-B3 A2-B2 A3-B1 A1-B1 A2-B3 A3-B2 A1-B2 A2-B1 A3-B3 Input2 3OutputA1-C2 A2-B1 B2-C1 A2-C2 B1-C1 A1-B2 A2-C1 B1-C2 A1-C1 B2-C2 A1-B1 A2-B2 Input1 5OutputA1-D1 C1-E1 A1-C1 B1-E1 A1-E1 B1-D1 B1-C1 D1-E1 A1-B1 C1-D1 "}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ n, m \\in \\mathbb{Z}^+ $ with $ 1 \\leq n \\leq 25 $, $ 2 \\leq m \\leq 25 $, $ nm \\leq 100 $.  \nLet $ 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}\\} $.  \nLet $ P = \\bigcup_{i=1}^m T_i $ be the set of all players, with $ |P| = nm $.  \n\n**Constraints**  \n1. Each player must play exactly $ (m-1)n $ games, each against a player from a different team.  \n2. In each round, a player may participate in at most one game.  \n3. Each player may have at most one bye (i.e., no game) across the entire schedule.  \n4. No intra-team games are allowed.  \n5. Each game is an unordered pair $ \\{P_{i,a}, P_{j,b}\\} $ with $ i \\neq j $.  \n\n**Objective**  \nConstruct a set of rounds $ R_1, R_2, \\dots, R_r $, where $ r \\leq (m-1)n + 1 $, such that:  \n- Each round is a set of disjoint games (no player appears in more than one game per round).  \n- Every valid inter-team pair $ (P_{i,a}, P_{j,b}) $ with $ i \\neq j $ appears in exactly one round.  \n- 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.","simple_statement":"Schedule matches so each player plays every player not on their team exactly once, with at most one bye per player, using as few rounds as possible. Output one round per line, with games as \"X-Y\".","has_page_source":false}