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)

#![allow(unused_imports)]

mod pcl {

}



use std::cmp::{max, min};

fn main() {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let mut it = s.split_whitespace();
    let n = it.next().unwrap().parse::<i32>().unwrap();
    let x = it.next().unwrap().parse::<i32>().unwrap() - 1;
    let y = it.next().unwrap().parse::<i32>().unwrap() - 1;

    let dist = |a, b| {
        let v_loop = y - x + 1;
        let skip = y - x - 1;
        match (a <= x, y <= b) {
            (true, true) => b - a - skip,
            (true, false) => (x - a) + min(b - x, v_loop - (b - x)),
            (false, true) => min(y - a, v_loop - (y - a)) + (b - y),
            (false, false) => min(b - a, v_loop - (b - a)),
        }
    };

    let mut count = vec![0; n as usize];
    for a in 0..n {
        for b in (a + 1)..n {
            let d = dist(a, b);
            debug_assert!(0 <= d && d < n);
            count[dist(a, b) as usize] += 1;
        }
    }

    for k in 1..n {
        println!("{}", count[k as usize]);
    }
}