Leetcode 2954. Count the Number of Infection Sequences

Count the number of distinct orders in which all uninfected people can become infected when infection spreads only to adjacent people from the initially sick positions; this is a combinatorics problem that partitions the line into segments between sick indices and counts interleavings of infections (multinomial) with extra multiplicative factors for middle segments due to bidirectional spread, modulo 1e9+7.