P24341 [AtCoder] Operations on a Matrix
提高-
题目描述

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.

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.

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.

Sample Input 1

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

Sample Output 1

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 \ $\end{pmatrix}$

Sample Input 2

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

Sample Output 2

9000000000

Sample Input 3

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

Sample Output 3

6
5
5
13
10
0

输入格式

见题面 Input 部分

输出格式

见题面 Output 部分

样例输入
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
样例输出
1 2 2 5 3 4