CF1129D.Isolation

普及/提高-

通过率：0%

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题目描述

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 $998\,244\,353$ .

输入格式

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 $a$ .

输出格式

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

输入输出样例

输入#1
```
3 1
1 1 2
```
输出#1
```
3
```
输入#2
```
5 2
1 1 2 1 3
```
输出#2
```
14
```
输入#3
```
5 5
1 2 3 4 5
```
输出#3
```
16
```

说明/提示

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 $[1, 2]$ .

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