D. Isolation
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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

Examples
Input
3 1
1 1 2
Output
3
Input
5 2
1 1 2 1 3
Output
14
Input
5 5
1 2 3 4 5
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 $$$[1, 2]$$$.