A12408. Isolation

Find the number of ways to divide an array $a$ of $n$ integers into any number of disjoint non-empty segments so that, in each segment, there exist at most $k$ distinct integers that appear exactly once.

Since the answer can be large, find it modulo $998\,244\,353$ .

The first line contains two space-separated integers $n$ and $k$ ( $1 \leq k \leq n \leq 10^5$ ) — the number of elements in the array $a$ and the restriction from the statement.

The following line contains $n$ space-separated integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq n$ ) — elements of the array $a$ .

The first and only line contains the number of ways to divide an array $a$ modulo $998\,244\,353$ .

In the first sample, the three possible divisions are as follows.

- $[[1], [1], [2]]$
- $[[1, 1], [2]]$
- $[[1, 1, 2]]$

Division $[[1], [1, 2]]$ is not possible because two distinct integers appear exactly once in the second segment $[1, 2]$ .