P10266 Efficient Cleaning

A design concept diagram of the cleaning bomb: 

Mahiro's room is too large, but as a shut-in, she is too lazy to clean it, so Mihari invented a cleaning bomb for Mahiro to use. Mahiro's room consists of tiles arranged in $n$ rows and $m$ columns. The amount of dust on the tile in row $i$ and column $j$ is $a_{i,j}$. Mahiro will use the cleaning bomb $k$ times. In the $i$-th use, she uses a cleaning bomb with energy value $p_i$ on the tile at row $x_i$, column $y_i$. This decreases the dust on $(x_i,y_i)$ by ${p_i}^2$, decreases the dust on the tiles in the first outer ring around $(x_i,y_i)$ by $(p_i-1)^2$, decreases the dust on the tiles in the second outer ring by $(p_i-2)^2$, $\cdots$, and decreases the dust on the tiles in the $(p_i-1)$-th outer ring by $1$. Of course, the dust amount cannot be negative, so if before an operation, the dust on a tile is smaller than the amount it should be decreased by, then its dust amount becomes $0$. Please output the dust amount on each tile after Mahiro finishes using the cleaning bomb $k$ times.

The first line contains three integers $n,m,k$, representing the number of tile rows, tile columns, and the number of operations. Next, there are $n$ lines, each containing $m$ integers. The integer in row $i$ and column $j$ is $a_{i,j}$, describing the dust amount on each tile. Next, there are $k$ lines. The $i$-th line contains three integers $x_i,y_i,p_i$, describing one operation.

Output $n$ lines, each containing $m$ integers. The integer in row $i$ and column $j$ represents the final dust amount on tile $(i,j)$.

**Sample** $\mathbf{1}$ **Explanation** In the first operation, a “cleaning bomb” with energy value $2$ is used on tile $(2,4)$, which decreases the dust on $(2,4)$ by $4$, and decreases the dust on $(1,3),(1,4),(1,5),(2,3),(2,5),(3,3),(3,4),(3,5)$ by $1$. In the second operation, a “cleaning bomb” with energy value $2$ is used on tile $(3,3)$, which decreases the dust on $(3,3)$ by $4$, and decreases the dust on $(2,2),(2,3),(2,4),(3,2),(3,4),(4,2),(4,3),(4,4)$ by $1$. **Constraints** For all testdata, $1\leq n,m,p_i\leq 10^3$, $1\leq k\leq 10^6$, $0\leq a_{i,j}\leq 10^{12}$, $1\leq x_i\leq n$, $1\leq y_i\leq m$. This problem has $11$ test points and **uses bundled tests**. The subtasks and test point allocation are as follows: | Subtask ID | Test Point ID | Special Property | Score | | :-: | :-: | :-: | :-: | | $0$ | $1\sim 4$ | $n,m,k\leq 300$ | $10$ | | $1$ | $5$ | $p_i\leq 3$ | $10$ | | $2$ | $6\sim 7$ | $k\leq 10^3$ | $20$ | | $3$ | $8\sim 9$ | $n,m\leq 300$ | $20$ | | $4$ | $10\sim 11$ | No special limits | $40$ | Translated by ChatGPT 5