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 ll long long int
#define pb push_back
#define translow transform(s.begin(),s.end(),s.begin(),::tolower);
#define transup transform(s.begin(),s.end(),s.begin(),::toupper);
#define endl "\n"
#define fast ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
ll mod=1e9+7;
ll n;
 vector<ll>adj[100000];
 
 
       

int main() {
                fast
                // #ifndef ONLINE_JUDGE
                // freopen("input.txt","r",stdin);
                // freopen("output.txt","w",stdout);
                // #endif
                 
                  cin>>n;
vector<ll>ans;
                  ans.resize(n+1,0);
                  vector<ll>adj[n+1];
                  for(ll i=1;i<n;i++)
                  {
                    adj[i].pb(i+1);
                    adj[i+1].pb(i);
                  }
                  ll x,y;
                  cin>>x>>y;
                  adj[x].pb(y);
                  adj[y].pb(x);
                  
                  for(ll i=1;i<=n;i++)
                  {

                   queue<ll>q;
                   ll source=i;
            q.push(source);
            vector<ll>dist(n+1,-1);
            dist[source]=0;
            while(!q.empty())
            {
                ll cn=q.front();
                q.pop();
                for(auto it:adj[cn])
                {
                    if(dist[it]==-1)
                    {
                        dist[it]=dist[cn]+1;
                        q.push(it);
                    }
                }
            }

            for(ll i=1;i<=n;i++)
            {
                ans[dist[i]]+=1;
            }
                  }
                  for(ll i=1;i<n;i++)
                    cout<<ans[i]/2<<" ";


                return 0;
            }