in Homers school n student love club initially m club n student exactly club in word a_i student ith club 1 leq leq m a_1a_2dotsa_m nThe n student unfriendly day choose uniformly random n student get angry the student get angry follow thing with probability frac 1 2 leave current club create new club join there student new club create with probability frac 1 2 create new club in case change club new possibly club currently probability proportional number student formally suppose k club b_i student ith club 1 leq leq k student get angry he leave current club join ith club probability frac b_i n we note club student join student get angry join club probability 0 accord statementHomer wonder expect number day student club timeWe prove answer represent rational number frac p q gcdp q 1 therefore ask find value pq1 bmod 998244353 it show q bmod 998244353 neq 0 give constraint problem