Slay the Spire is a game primarily about survival, collecting cards, and building a powerful deck to wipe out your foes.Recently, Colin got interested in a special card : 'Alpha'.Playing the 'Alpha' card will shuffle a 'Beta' into the draw pile.Playing the 'Beta' card will shuffle an 'Omega' card into the draw pile.Playing the 'Omega' card will generate the final Omega buff -- destroy your enemies, and achieve ultimate victory.However, Colin always has poor luck during the game. So he wants to calculate at least how many rounds have been passed, no matter how bad his luck is, he will definitely win. To simplify the problem, we describe it as follows:. At the beginning, there are onlynan_ana 'Alpha' card , nbn_bnb'Beta' card and non_ono'Omega' Card in the draw pile.In each round, the system first randomly shufflesthe entire draw pile, then Colin takes out kktext{ }k cards at the top of the draw pile:. If there are at least one 'Omega' card among the kkk cards, Colin win the game immediately.Please calculate at least how many rounds have been passed, no matter how bad Colin's luck is, he will definitely win.
Slay the Spire is a game primarily about survival, collecting cards, and building a powerful deck to wipe out your foes. Recently, Colin got interested in a special card : 'Alpha'. Playing the 'Alpha' card will shuffle a 'Beta' into the draw pile. Playing the 'Beta' card will shuffle an 'Omega' card into the draw pile. Playing the 'Omega' card will generate the final Omega buff -- destroy your enemies, and achieve ultimate victory. However, Colin always has poor luck during the game. So he wants to calculate at least how many rounds have been passed, no matter how bad his luck is, he will definitely win. To simplify the problem, we describe it as follows: At the beginning, there are only nan_ana 'Alpha' card , nbn_bnb 'Beta' card and non_ono 'Omega' Card in the draw pile. In each round, the system first randomly shuffles the entire draw pile, then Colin takes out k (k≤na+nb+no)ktext{ }(kle n_a + n_b + n_o )k (k≤na+nb+no) cards at the top of the draw pile: If there are at least one 'Omega' card among the kkk cards, Colin win the game immediately. Otherwise, Colin will play the kkk cards taken out in an arbitrary order. (Playing the 'Alpha' card will shuffle a 'Beta' into the draw pile. Playing the 'Beta' card will shuffle an 'Omega' card into the draw pile.) Please calculate at least how many rounds have been passed, no matter how bad Colin's luck is, he will definitely win.
