Isolation

Description:

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 $$$998\,244\,353$$$.

Sample Input:

3 1
1 1 2

Sample Output:

3

Sample Input:

5 2
1 1 2 1 3

Sample Output:

14

Sample Input:

5 5
1 2 3 4 5

Sample Output:

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 $$$[1, 2]$$$.