The Films

In "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:

1. Empty the storage.
2. Put k_i ⋅ m films into the storage, k_i films for each ending.
3. 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 ⋅ A_i is always an integer. Print for each month P_i ⋅ A_i \pmod {998244353}.

998244353 is a prime number and it is equal to 119 ⋅ 2^{23} + 1.

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

Input

The first line contains three integers n, m, and q (1 ≤ n, m, q ≤ 10^5, n+q≤ 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, …, e_n (1≤ e_i≤ 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 ≤ l_i ≤ r_i ≤ n, 0 ≤ k_i ≤ 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.

Examples

Input

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

Output

6 26730 12150 4860

Input

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

Output

494942218 13125 151632

Note

In the first sample in the second query, after adding 2 ⋅ 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}, …, 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 (26730/2162160 ⋅ 2162160) mod 998244353 = 26730.

inputFormat

Input

The first line contains three integers n, m, and q (1 ≤ n, m, q ≤ 10^5, n+q≤ 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, …, e_n (1≤ e_i≤ 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 ≤ l_i ≤ r_i ≤ n, 0 ≤ k_i ≤ 10^5) — the i-th query.

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

outputFormat

Output

Print the answer for each question in a separate line.

Examples

Input

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

Output

6 26730 12150 4860

Input

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

Output

494942218 13125 151632

Note

In the first sample in the second query, after adding 2 ⋅ 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}, …, 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 (26730/2162160 ⋅ 2162160) mod 998244353 = 26730.

样例

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

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