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 $1 \\leq j \\leq Q$.

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.

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.

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