Isolation
Description
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 $998\,244\,353$.
Input
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 $a$.
Output
The first and only line contains the number of ways to divide an array $a$ modulo $998\,244\,353$.
Samples
3 1
1 1 2
3
5 2
1 1 2 1 3
14
5 5
1 2 3 4 5
16
Note
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 $[1, 2]$.