A popular TV show ``Kak? Zachem? Pochemu?'' highlights a team of six players working together to solve challenging questions. Players sit around a circular table divided into $n$ sectors numbered clockwise from $1$ to $n$. At the start of the game, each sector contains an envelope with a question to be answered.

Each round, the spinning top at the center of the table chooses a sector of the table uniformly at random. If the chosen sector contains an envelope, the host opens it and reads the question inside. If there is no envelope in the chosen sector, the host opens the next envelope in the clockwise direction from the chosen sector instead. After the round, the opened envelope is removed from the table.

Tonight, the audience's favorite team is playing. They have already played $n - k$ rounds out of $n$, so there are $k$ envelopes remaining on the table. Things are not looking good for the team~--- one more incorrect answer will send them home. One of the questions is a special, notoriously hard question called ``Hyperblitz''. The team is confident they can answer each of the remaining questions except ``Hyperblitz''. Find the expected number of rounds they will play, modulo $998\,244\,353$ (see the Output section for details).