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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
  list($n, $x, $y) = explode(" ", trim(fgets(STDIN)));

  $a = [];

  for($i=1;$i<=$n;$i++){
    if(!isset($a[$i])){
      $a[$i]=0;
    }
    for($j=$i+1;$j<=$n;$j++){
      if($i <= $x && $j <= $x){
//        echo "1:".$j." ".$i.PHP_EOL;
        $dist = $j-$i;
      }
      else if($i <= $x && ($j > $x && $j < $y)){
//        echo "2:".$j." ".$i.PHP_EOL;
        $dist = min($j-$i, $x-$i+$y-$j+1);
      }
      else if($i <= $x && $j >= $y){
//        echo "3:".$j." ".$i.PHP_EOL;
        $dist = $x-$i+$j-$y+1;
      }
      else if(($i > $x && $i < $y) && ($j > $x && $j < $y)){
//        echo "4:".$j." ".$i.PHP_EOL;
        $dist = min($j-$i, $i-$x+$y-$j+1);
      }
      else if(($i > $x && $i < $y) && $j >= $y){
        $dist = min($j-$i, $i-$x+$j-$y+1);
      }
      else if($i >= $y){
//        echo "5:".$j." ".$i.PHP_EOL; 
        $dist = $j-$i;
      }
      if(!isset($a[$dist])){
        $a[$dist]=0;
      }
//      if($dist==1){
//        echo $i." ".$j.PHP_EOL;
//      }
      $a[$dist]++;
    }
  }
  for($i=1;$i<=$n-1;$i++){
    echo $a[$i].PHP_EOL;
  }