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)

fn main() {
    let (n, x, y): (i32, i32, i32) = input();
    let ans = solve(n, x, y);
    for a in ans.iter() { println!("{}", a); }
}

fn input() -> (i32, i32, i32) {
    let mut buf = String::from("");
    buf.pop();
    std::io::stdin().read_line(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let n: i32 = iter.next().unwrap().parse().unwrap();
    let x: i32 = iter.next().unwrap().parse().unwrap();
    let y: i32 = iter.next().unwrap().parse().unwrap();
    (n, x, y)
}

fn solve(n: i32, x: i32, y: i32) -> Vec<usize> {
    let mut ans: Vec<usize> = vec![0usize; (n-1) as usize];
    for i in 1..n {
        for j in (i+1)..(n+1) {
            // min{|j − i|, |X − i| + 1 + |j − Y |, |Y − i| + 1 + |j − X|}
            let dis = std::cmp::min(j - i, (i - x).abs() + 1 + (j - y).abs()) as usize;
            ans[dis-1] += 1 as usize;
        }
    }
    ans
}