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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define FOR(i, s, e) for (int i = (int)(s); i <= (int)(e); i++)
#define printYesNo(is_ok) puts(is_ok ? "Yes" : "No");
#define SORT(v) sort(v.begin(), v.end());
#define RSORT(v) sort(v.rbegin(), v.rend());
#define REVERSE(v) reverse(v.begin(), v.end());

template <typename T>
void printlnVector(T v)
{
  rep(i, v.size())
  {
    cout << v[i] << endl;
  }
}

template <typename T>
void printVector(T v)
{
  rep(i, v.size())
  {
    cout << v[i] << " ";
  }
  cout << endl;
}

int main()
{
  int N, X, Y;
  cin >> N >> X >> Y;

  vector<int> ans(N - 1, 0);
  for (int i = 0; i < N; i++)
  {
    for (int j = i + 1; j < N; j++)
    {
      int posi = i + 1;
      int posj = j + 1;
      int dist1 = posj - posi;
      int dist2 = abs(X - posi) + abs(Y - posj) + 1;
      int dist3 = abs(Y - posi) + abs(X - posj) + 1;
      int dist = min({dist1, dist2, dist3});
     // cout << i << "->" << j << ":" << dist1 << ", " << dist2 << ", " << dist3 << endl;
      ans[dist - 1]++;
    }
  }

  printlnVector(ans);
  return 0;
}