Problem Statement

Find the number, modulo 998244353, of integer sequences $A = (A_1, \dots, A_N)$ of length N that satisfy all of the following conditions:

• $0 \leq A_i \leq M$ for all i such that $1 \leq i \leq N$.
• The maximum value of $A_{L_j}, \dots, A_{R_j}$ is X_j for all j such that $1 \leq j \leq Q$.

Input

Input is given from Standard Input in the following format:
N M Q
L_1 R_1 X_1
$\vdots$
L_Q R_Q X_Q

Output

Print the answer.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq M \lt 998244353$
• $1 \leq Q \leq 2 \times 10^5$
• $1 \leq L_i \leq R_i \leq N$ $, (1 \leq i \leq Q)$
• $1 \leq X_i \leq M$ $, (1 \leq i \leq Q)$
• All values in input are integers.

Sample Input 1

3 3 2
1 2 2
2 3 3

Sample Output 1

5

A = (0, 2, 3), (1, 2, 3), (2, 0, 3), (2, 1, 3), (2, 2, 3) satisfy the conditions.

Sample Input 2

1 1 1
1 1 1

Sample Output 2

1

Sample Input 3

6 40000000 3
1 4 30000000
2 6 20000000
3 5 10000000

Sample Output 3

135282163

见题面 Input 部分

见题面 Output 部分