Team $A$ and team $B$ play a series. The first team to win three games wins the series. Before each game, each team is equally likely to win each game, there are no ties, and the outcomes of the individual games are independent. If it turns out that team $B$ won the second game and team $A$ won the series, what is the conditional probability that team $B$ won the first game? The answer is in the form \(\frac{k}{m}\). Please provide the value of k + m.

Let's think step by step and output the final answer within \boxed{}.
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