Background

Related multiple-choice and true/false problems: https://ti.luogu.com.cn/problemset/1107.

Problem Description

On a mysterious fantasy continent, there are $n$ ancient and magical mazes, numbered from $1$ to $n$. Between some mazes, you can travel directly both ways; between some others, you can travel from one maze to another, but cannot come back. The player Xiao Yang wants to challenge different mazes, and he decides to start from maze $m$. Now he needs your help to count: how many mazes can directly reach maze $m$, how many other mazes maze $m$ can directly reach, and output the sum of these two numbers.

Note that for maze $i$ ($1 \leq i \leq n$), it can always directly reach itself.

Input Format

The first line contains two integers $n$ and $m$, representing the total number of maze nodes and the index of the specified starting maze.
The next $n$ lines each contain $n$ integers, describing the relations between mazes. For the integer in row $i$, column $j$, $1$ means you can directly go from maze $i$ to maze $j$, and $0$ means you cannot directly go.

Output Format

Output one line with three integers separated by spaces: the number of other mazes that maze $m$ can directly reach, the number of mazes that can directly reach maze $m$, and the sum of these two counts.

6 4
1 1 0 1 0 0
0 1 1 0 0 0
1 0 1 0 0 1
0 0 1 1 0 1
0 0 0 1 1 0
1 0 0 0 1 1

3 3 6

Hint

Explanation of Sample 1

Maze $4$ can directly reach mazes $3,4,6$, for a total of $3$.
Mazes that can directly reach maze $4$ are $1,4,5$, for a total of $3$.

In total, there are $6$.

Constraints

For all testdata, it is guaranteed that $1 \leq m \leq n \leq 1000$.

Translated by ChatGPT 5