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 $$$998\,244\,353$$$.
3 1 1 1 2
5 2 1 1 2 1 3
5 5 1 2 3 4 5
In the first sample, the three possible divisions are as follows.
Division $$$[, [1, 2]]$$$ is not possible because two distinct integers appear exactly once in the second segment $$$[1, 2]$$$.