Problem:
Score : 400 points

Problem Statement

We have an undirected graph G with N vertices numbered 1 to N and N edges as follows:

For each i=1,2,...,N-1, there is an edge between Vertex i and Vertex i+1.

There is an edge between Vertex X and Vertex Y.

For each k=1,2,...,N-1, solve the problem below:

Find the number of pairs of integers (i,j) (1 \leq i < j \leq N) such that the shortest distance between Vertex i and Vertex j in G is k.

Constraints

3 \leq N \leq 2 \times 10^3

1 \leq X,Y \leq N

X+1 < Y

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N X Y

Output

For each k=1, 2, ..., N-1 in this order, print a line containing the answer to the problem.

Sample Input 1

5 2 4

Sample Output 1

5
4
1
0

The graph in this input is as follows:

There are five pairs (i,j) (1 \leq i < j \leq N) such that the shortest distance between Vertex i and Vertex j is 1: (1,2)\,,(2,3)\,,(2,4)\,,(3,4)\,,(4,5).

There are four pairs (i,j) (1 \leq i < j \leq N) such that the shortest distance between Vertex i and Vertex j is 2: (1,3)\,,(1,4)\,,(2,5)\,,(3,5).

There is one pair (i,j) (1 \leq i < j \leq N) such that the shortest distance between Vertex i and Vertex j is 3: (1,5).

There are no pairs (i,j) (1 \leq i < j \leq N) such that the shortest distance between Vertex i and Vertex j is 4.

Sample Input 2

3 1 3

Sample Output 2

3
0

The graph in this input is as follows:

Sample Input 3

7 3 7

Sample Output 3

7
8
4
2
0
0

Sample Input 4

10 4 8

Sample Output 4

10
12
10
8
4
1
0
0
0

Solution in Rust (1.15.1) (judge verdict: Time Limit Exceeded)

use std::cmp::min;


fn main() {
    let (n, x, y) = read_tuple();

    let mut graph = vec![vec![1e4 as i64; n]; n];
    for i in 0..n {
        graph[i][i] = 0;
    }
    for i in 0..(n-1) {
        graph[i][i+1] = 1;
        graph[i+1][i] = 1;
    }
    graph[x-1][y-1] = 1;
    graph[y-1][x-1] = 1;

    for k in 0..n {
        for i in 0.. n {
            for j in 0..n {
                graph[i][j] = min(graph[i][j], graph[i][k] + graph[k][j]);
            }
        }
    }

    let mut counter = vec![0; n];
    for line in graph.iter() {
        for w in line.iter() {
            if (*w as usize) < n {
                counter[*w as usize] += 1;
            }
        }
    }

    for c in counter.iter().skip(1) {
        println!("{:?}", c / 2);
    }

}
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}
fn read_tuple<T: std::str::FromStr + Copy>() -> (T, T, T) {
    let temp = read_vec();
    (temp[0], temp[1], temp[2])
}