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 JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";

function d(a, b, x, y) {
  if (a < x) {
    if (b > y) {
      return b - a - (y - x) + 1;
    }

    return Math.min(b - a, x - a + y - b + 1);
  }

  if (b > y) {
    return Math.min(b - a, b - y + a - x + 1);
  }

  return Math.min(b - a, y - b + a - x + 1);
} // inputに入力データ全体が入る


function Main(input) {
  var a = input.split(' ').map(function (aa) {
    return parseInt(aa);
  });
  var n = a[0];
  var x = a[1];
  var y = a[2];
  var ans = Array.from({
    length: n - 1
  }, function (v, i) {
    return 0;
  });

  for (var j = 1; j < n; j++) {
    for (var k = j + 1; k <= n; k++) {
      ans[d(j, k, x, y) - 1]++;
    }
  }

  for (var _i = 0, _ans = ans; _i < _ans.length; _i++) {
    var _a = _ans[_i];
    console.log(_a);
  }
} //*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）


Main(require("fs").readFileSync("/dev/stdin", "utf8"));