CF1906F.Maximize The Value

You are given a one-based array consisting of $N$ integers: $A_1, A_2, \cdots, A_N$ . Initially, the value of each element is set to $0$ .

There are $M$ operations (numbered from $1$ to $M$ ). Operation $i$ is represented by $\langle L_i, R_i, X_i \rangle$ . If operation $i$ is executed, all elements $A_j$ for $L_i \leq j \leq R_i$ will be increased by $X_i$ .

You have to answer $Q$ independent queries. Each query is represented by $\langle K, S, T \rangle$ which represents the following task. Choose a range $[l, r]$ satisfying $S \leq l \leq r \leq T$ , and execute operations $l, l + 1, \dots, r$ . The answer to the query is the maximum value of $A_K$ after the operations are executed among all possible choices of $l$ and $r$ .

The first line consists of two integers $N$ $M$ ( $1 \leq N, M \leq 100\,000$ ).

Each of the next $M$ lines consists of three integers $L_i$ $R_i$ $X_i$ ( $1 \leq L_i \leq R_i \leq N; -100\,000 \leq X_i \leq 100\,000$ ).

The following line consists of an integer $Q$ ( $1 \leq Q \leq 100\,000$ ).

Each of the next $Q$ lines consists of three integers $K$ $S$ $T$ ( $1 \leq K \leq N; 1 \leq S \leq T \leq M$ ).

For each query, output in a single line, an integer which represent the answer of the query.

Explanation for the sample input/output #1

For query $1$ , one of the solutions is to execute operation $4$ and $5$ .

For query $2$ , one of the solutions is to execute operation $4$ , $5$ , and $6$ .

For query $3$ , the only solution is to execute operation $3$ .

For query $4$ , the only solution is to execute operation $1$ .

For query $6$ , the only solution is to execute operation $2$ .