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F - Operations on a Matrix

Score : $500$ points

Problem Statement

We have an $N \times M$ matrix, whose elements are initially all $0$.

Process $Q$ given queries. Each query is in one of the following formats.

• 1 l r x : Add $x$ to every element in the $l$-th, $(l+1)$-th, $\ldots$, and $r$-th column.
• 2 i x: Replace every element in the $i$-th row with $x$.
• 3 i j: Print the $(i, j)$-th element.

Constraints

• $1 \leq N, M, Q \leq 2 \times 10^5$
• Every query is in one of the formats listed in the Problem Statement.
• For each query in the format 1 l r x, $1 \leq l \leq r \leq M$ and $1 \leq x \leq 10^9$.
• For each query in the format 2 i x, $1 \leq i \leq N$ and $1 \leq x \leq 10^9$.
• For each query in the format 3 i j, $1 \leq i \leq N$ and $1 \leq j \leq M$.
• At least one query in the format 3 i j is given.
• All values in input are integers.

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Input

Input is given from Standard Input in the following format:

$N$ $M$ $Q$

$\mathrm{Query}_1$

$\vdots$

$\mathrm{Query}_Q$

$\mathrm{Query}_i$, which denotes the $i$-th query, is in one of the following formats:

``` $1$ $l$ $r$ $x$ ``` ``` $2$ $i$ $x$ ``` ``` $3$ $i$ $j$ ```

Output

For each query in the format 3 i j, print a single line containing the answer.

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3 3 9
1 1 2 1
3 2 2
2 3 2
3 3 3
3 3 1
1 2 3 3
3 3 2
3 2 3
3 1 2

1
2
2
5
3
4

The matrix transitions as follows.

$\begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ \end{pmatrix} \rightarrow \begin{pmatrix} 1 & 1 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 0 \\ \end{pmatrix} \rightarrow \begin{pmatrix} 1 & 1 & 0 \\ 1 & 1 & 0 \\ 2 & 2 & 2 \\ \end{pmatrix} \rightarrow \begin{pmatrix} 1 & 4 & 3 \\ 1 & 4 & 3 \\ 2 & 5 & 5 \\ \end{pmatrix}$

---

1 1 10
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
3 1 1

9000000000

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10 10 10
1 1 8 5
2 2 6
3 2 1
3 4 7
1 5 9 7
3 3 2
3 2 8
2 8 10
3 8 8
3 1 10

6
5
5
13
10
0