4582 F

Given the sequence a[0 . . . n] ,ask the value of

mod 998241383

wikipedia: k-permutations of n are the different ordered arrangements of a k-element subset of an n-set (sometimes called variations or arrangements in the older literature). These objects are also known as partial permutations or as sequences without repetition, terms that avoid confusion with the other, more common, meaning of ”permutation”. The number of such k-permutations of n is denoted variously by such symbols as Pkn or P(n, k),and its value is given by the product P(n, k) = n · (n − 1) · (n − 2)· · ·(n − k + 1) | {z } k factors ,which is 0 when k > n, and otherwise is equal to n! (n−k)! .

Assume that P(i, 0) = 1, P(0, 0) = 1