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 C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
#define SORT(a) sort((a).begin(), (a).end())
#define RSORT(a) reverse((a).begin(), (a).end())
#define rep(i, n) for (int i = 0; i < n; i++)
#define all(a) ((a).begin(), (a).end())
typedef long long ll;
// const long long INF = 1LL << 60;
const int INF = 1010101010;
using Graph = vector<vector<int>>;
const int MOD = 1000000007;

int main() {
  int n, x, y;
  cin >> n >> x >> y;
  vector<vector<int>> d(n, vector<int>(n, INF));

  for (int i = 0; i < n; i++) {
    d[i][i] = 0;
  }

  int cnt = 0;

  for (int i = 0; i < n - 1; i++) {
    d[i][i + 1] = 1;
    d[i + 1][i] = 1;
  }
  x--;
  y--;
  d[x][y] = 1;
  d[y][x] = 1;
  for (int k = 0; k < n; k++) {      // 経由する頂点
    for (int i = 0; i < n; i++) {    // 始点
      for (int j = 0; j < n; j++) {  // 終点
        d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
      }
    }
  }
  vector<int> ans(n);
  for (int i = 0; i < n - 1; i++) {
    for (int j = i + 1; j < n; j++) {
      ans[d[i][j]]++;
    }
  }
  for (int i = 1; i < n; i++) cout << ans[i] << endl;
}