H. The Filmstime limit per test5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputIn "The Man in the High Castle" world, there are m different film endings. Abendsen owns a storage and a shelf. At first, he has n ordered films on the shelf. In the i-th month he will do: Empty the storage. Put k_i \cdot m films into the storage, k_i films for each ending. He will think about a question: if he puts all the films from the shelf into the storage, then randomly picks n films (from all the films in the storage) and rearranges them on the shelf, what is the probability that sequence of endings in [l_i, r_i] on the shelf will not be changed? Notice, he just thinks about this question, so the shelf will not actually be changed.Answer all Abendsen's questions.Let the probability be fraction P_i. Let's say that the total number of ways to take n films from the storage for i-th month is A_i, so P_i \cdot A_i is always an integer. Print for each month P_i \cdot A_i \pmod {998244353}.998244353 is a prime number and it is equal to 119 \cdot 2^{23} + 1.It is guaranteed that there will be only no more than 100 different k values.InputThe 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.OutputPrint the answer for each question in a separate line.ExamplesInput6 4 41 2 3 4 4 41 4 01 3 21 4 21 5 2Output626730121504860Input5 5 31 2 3 4 51 2 1000001 4 43 5 5Output49494221813125151632NoteIn 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.
Input6 4 41 2 3 4 4 41 4 01 3 21 4 21 5 2
Output626730121504860
['brute force', '*3300']