{"problem":{"name":"G. Game Scheduling","description":{"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 play","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10193G"},"statements":[{"statement_type":"Markdown","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## Input\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\n## Output\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[samples]","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"**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.","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10193G","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}