Nim

Let's play a traditional game of Nim. You and I are seated at a table, with a hundred stones in front of us (the exact number of stones is known). We take turns; each turn, a player can take one to four stones from the pile. You play first. The player who takes the last stone loses.

In this game, there is a winning strategy. First, you take $4$ stones, leaving $96$ in the pile. No matter how I play, there will be between $92$ and $95$ stones left. Then, after your turn, you leave me with $91$ stones (verify this is always possible). By repeating this procedure, you always leave me with 5k+1 stones, so I am forced to take the last stone and lose. If, instead, there were $101$ stones initially, I would have a winning strategy, and you would always lose.

Let's generalize the game. First, suppose it's a team game. Each team has $n$ players; the $2n$ players are seated around the table, with each player having opponents on both sides. Players take turns around the table, so the teams alternate moves. Second, let each player have their own maximum number of stones they may take per turn (the minimum is always one). Thus, the game becomes asymmetric and possibly unfair.

When both teams play optimally, the outcome is fully determined by the initial number of stones and the maximum number each player may take on their turn. Thus, one team always has a winning strategy.

You are the coach of a team. For each game, the referee announces the initial number of stones and, for each player, the maximum number of stones they may take in one turn. Your team moves first. Decide whether your team has a winning strategy.