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;
typedef long long ll;
typedef vector<int> vi;
typedef vector<string> vs;
typedef vector<bool> vb;
typedef vector<char> vc;
typedef vector<vector<int>> vvi;
typedef vector<vector<string>> vvs;
typedef vector<vector<char>> vvc;
typedef vector<vector<bool>> vvb;
typedef pair<int,int> P;
#define vrep(v,n) for(int i=0;i<n;i++){cin >> v.at(i);} //配列vにn個の要素を入力する
#define rep(i, l, n) for (int i = l; i < (int)(n); i++)
#define repn(i, l, n) for (int i = l; i <= (int)(n); i++)
#define push_back pb

const int mod = 1000000007;
const int inf = 1e9;

int main(){
    int n, x, y;
    cin >> n >> x >> y;
    int v[n+1]={0};
    //処理

    for(int i = 1 ; i < n ; i++){
        for(int j = i+1 ; j <= n ; j++){
            int dis = 0;
            int a = j - i;
            int b = abs(x-i)+1+abs(y-j);
            int c = abs(x-j)+1+abs(y-i);
            dis = min({a,b,c});
            v[dis]++;
        }
    }
    repn(i, 1, n-1){
        cout << v[i] << endl;
    }
}