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<iostream>
#include<algorithm>
#include<cmath>
#include<map>
#include<queue>
#include<string>
#include<set>
#include<utility>
#include<vector>

using namespace std;
typedef long long ll;
#define rep(i, n) for(int i=0; i<n; i++)
#define per(i, n) for(int i=n-1; i>=0; i--)
#define reps(i, n) for(int i=1; i<n; i++)
#define pers(i, n)  for(int i=n-1; i>=1; i--)

const int INF = 1001001001;

void solve(){
  int n, x, y;  cin >> n >> x >> y;
  x--;  y--;
  vector<vector<int>> vec(n, vector<int>(n, 0));
  vector<int> ans(n, 0);
  for(int i=0; i<n; i++){
    bool isForked = i==x;
    for(int j=i+1; j<n; j++){
      vec[i][j]=vec[i][j-1]+1;
      if(j==x)  isForked=true;
      if(isForked && j==y)  vec[i][j]=vec[i][x]+1;
    }
    if(i>x){
      vec[i][y] = min(vec[i][y], i-x+1);
    }
    for(int j=y-1; j>max(i, x); j--){
      vec[i][j] = min(vec[i][j], vec[i][j+1]+1);
    }
    for(int j=y+1; j<n; j++){
      vec[i][j] = min(vec[i][j], vec[i][j-1]+1);
    }

    for(int j=i+1; j<n; j++){
      ans[vec[i][j]]++;
    }
  }

  reps(i, n){
    cout << ans[i] << endl;
  }
}

int main(){
  solve();
  return 0;
}