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<stdio.h>
//#include <bits/stdc++.h>
#include<vector>
#include<float.h>
#include<iomanip>
#include<algorithm>
#include<string>
#include<cstring>
#include<math.h>
#include<cmath>
#include<sstream>
#include<set>
#include<map>
#include<queue>
#include <cassert>
#include <cmath>
#include<cstdint>

#define INF 1e9
#define rep(i,n)for(int i=0;(i)<(int)(n);i++)
#define REP(i,a,b)for(int i=(int)(a);(i)<=(int)(b);i++)
#define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)std::cin>>i;
#define vec(type,n) vector<type>(n)
#define vvec(m,n) vector<vector<int>> (int(m),vector<int>(n))
#define ALL(a)  (a).begin(),(a).end()

using namespace std;
using ll = long long;
using Graph = vector<vector<int>>;
using P = pair<int,int>;

vector<int>bitSearch(int bit,int n){
    vector<int>S;
    rep(i,n)if(bit&(1<<i))S.push_back(i);
    return S;
}


int main(){
    int n;cin>>n;
    int d[n+50][n+50];
    rep(i,n)rep(j,n)d[i][j] = INF;
    Graph G(n+1);
    rep(i,n){
        G[i].push_back(i+1);
        G[i+1].push_back(i);
    }
    int x,y;cin>>x>>y;
    x--;y--;
    G[x].push_back(y);
    G[y].push_back(x);

    queue<int>que;
    rep(i,n-1){
        d[i][i] = 0;
        que.push(i);
        while(!que.empty()){
            int v = que.front();que.pop();
            for(auto nv : G[v]){
                //if(nv<i)continue;
                if(d[i][nv]!=INF)continue;
                d[i][nv] = min(d[i][nv],d[i][v]+1);
                que.push(nv);
            }
        }
    }
    vector<int>v(n,0);
    rep(i,n){
        for(int j=i+1;j<n;j++){
            if(d[i][j]==INF)continue;
            v[d[i][j]]++;
        }
    }
    rep(i,n-1)cout<<v[i+1]<<endl;
}