Description

Input

The first line contains three integers $n$, $m$, and $q$ ($1 \le n, m, q \le 10^5$, $n+q\leq 10^5$) — the number of films on the shelf initially, the number of endings, and the number of months.

The second line contains $n$ integers $e_1, e_2, \ldots, e_n$ ($1\leq e_i\leq m$) — the ending of the $i$-th film on the shelf.

Each of the next $q$ lines contains three integers $l_i$, $r_i$, and $k_i$ ($1 \le l_i \le r_i \le n, 0 \le k_i \le 10^5$) — the $i$-th query.

It is guaranteed that there will be only no more than $100$ different $k$ values.

Output

Print the answer for each question in a separate line.

6 4 4
1 2 3 4 4 4
1 4 0
1 3 2
1 4 2
1 5 2

6
26730
12150
4860

5 5 3
1 2 3 4 5
1 2 100000
1 4 4
3 5 5

494942218
13125
151632

Note

In the first sample in the second query, after adding $2 \cdot m$ films into the storage, the storage will look like this: $\{1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4\}$.

There are $26730$ total ways of choosing the films so that $e_l, e_{l+1}, \ldots, e_r$ will not be changed, for example, $[1, 2, 3, 2, 2]$ and $[1, 2, 3, 4, 3]$ are such ways.

There are $2162160$ total ways of choosing the films, so you're asked to print $(\frac{26730}{2162160} \cdot 2162160) \mod 998244353 = 26730$.