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: Accepted)

use std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char) 
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

// fn main() {
//     let n: i64 = read();
//     let x: i64 = read();
//     let y: i64 = read();
//     let mut ans: Vec<i64> = (1..n).map(|_| 0).collect();
//     for i in 1..n+1 {
//         for j in i+1..n+1 {
//             let mut min = j - i;
//             let mut tmp = (x-i).abs() + 1 + (j-y).abs();
//             if tmp < min {
//                 min = tmp;
//             }
//             tmp = (y-i).abs() + 1 + (j-x).abs();
//             if tmp < min {
//                 min = tmp;
//             }
//             //println!("{} {} {}", i, j, min);
//             ans[min as usize - 1] += 1;
//         }
//     }

//     for a in ans {
//         println!("{}", a);
//     }
// }

use std::collections::VecDeque;

fn main() {
    let n: i64 = read();
    let mut x: i64 = read();
    let mut y: i64 = read();
    x -= 1; y -= 1;
    let mut ans: Vec<i64> = (0..n).map(|_| 0).collect();
    let INF: i64 = 1001001001;
    for i in 0..n {
        let mut dist: Vec<i64> =  (0..n).map(|_| INF).collect();
        let mut q: VecDeque<i64> = VecDeque::new();
        push(i, 0, &mut dist, &mut q, INF);
        while !q.is_empty() {
            let v = q.pop_front().unwrap();
            let d = dist[v as usize];
            if v-1 >= 0 {
                push(v-1, d+1, &mut dist, &mut q, INF);
            }
            if v+1 < n {
                push(v+1, d+1, &mut dist, &mut q, INF);
            }
            if v == x {
                push(y, d+1, &mut dist, &mut q, INF);
            }
            if v == y {
                push(x, d+1, &mut dist, &mut q, INF);
            }
        }
        for j in 0..n {
            ans[dist[j as usize] as usize] += 1;
        }
    }
    for i in 1..n {
        ans[i as usize] /= 2;
        println!("{}", ans[i as usize]);
    }
}

fn push(i: i64, d: i64, dist: &mut Vec<i64>, q: &mut VecDeque<i64>, INF: i64) {
    if dist[i as usize] != INF {
        return;
    }
    dist[i as usize] = d;
    q.push_back(i);
}