201301: [AtCoder]ARC130 B - Colorful Lines

Problem Statement

We have an $H\times W$ grid. Initially, the squares are unpainted.

You will paint these squares. There are $C$ colors available, numbered $1, 2, \ldots, C$.

The painting process will be given as $Q$ queries. The $i$-th query contains integers $t_i, n_i, c_i$, which represents the following action.

• If $t_i = 1$: paint all squares in the $n_i$-th row with Color $c_i$.
• If $t_i = 2$: paint all squares in the $n_i$-th column with Color $c_i$.

Painting a square with Color $c$ makes the color of that square Color $c$, regardless of its previous state.

Find the number of squares painted in each of Color $1, 2, \ldots, C$ after the whole process.

Constraints

• $2\leq H\leq 10^9$
• $2\leq W\leq 10^9$
• $1\leq C\leq 3\times 10^5$
• $1\leq Q\leq 3\times 10^5$
• $t_i\in \{1,2\}$
• $1\leq n_i\leq H$ if $t_i = 1$
• $1\leq n_i\leq W$ if $t_i = 2$
• $1\leq c_i\leq C$

Input

Input is given from Standard Input in the following format:

$H$ $W$ $C$ $Q$
$t_1$ $n_1$ $c_1$
$\vdots$
$t_Q$ $n_Q$ $c_Q$

Output

Print a line containing the numbers of squares painted in Color $1, 2, \ldots, C$, with spaces in between.

Sample Input 1

4 5 6 5
1 1 6
1 3 3
2 2 4
2 4 2
1 1 2

Sample Output 1

0 8 3 3 0 0

The process changes the colors of the squares as follows. Here, . denotes an unpainted square.

.....   66666   66666   64666   64626   22222
.....   .....   .....   .4...   .4.2.   .4.2.
.....   .....   33333   34333   34323   34323
.....   .....   .....   .4...   .4.2.   .4.2.

Sample Input 2

1000000000 1000000000 3 5
1 1 2
1 2 2
1 3 2
1 4 2
1 5 2

Sample Output 2

0 5000000000 0