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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
int zet(int a, int b){
  if(a-b>=0){
    return a-b;
  }
  if(a-b<0){
    return b-a;
  }
}
int main(){
  int N, X, Y;
  vector<int> vec(N+1);
  cin >> N >> X >> Y;
  vector<vector<int>> A(N+1,vector<int>(N+1));
  for(int i=1;i<N;i++){
    for(int j=1;j<N+1;j++){
      A.at(i).at(j)=min(zet(i,j), min(zet(X,i)+zet(Y,j)+1, zet(X,j)+zet(Y,i)+1));
    }//A.at(i).at(j)=(i,j)の最短距離
  }
    for(int i=1;i<N;i++){
      for(int j=1;j<N+1;j++){
        vec.at(A.at(i).at(j))++;
        }
      }
    for(int i=1;i<N;i++){
      cout << vec.at(i) << endl;
      cout << endl;
    }
}