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<ll> vl;typedef vector<vl> vvl;typedef pair<ll,ll> pl;typedef vector<pl> vp;const ll INF=1001001001;const ll LINF=1001001001001001001;const ll D4[]={0,1,0,-1,0};const ll D8[]={0,1,1,0,-1,-1,1,-1,0};template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return 1;}return 0;}template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return 1;}return 0;}
#define fore(i,a,b) for(ll i=(ll)(a);i<=(ll)(b);++i)
#define rep(i,n) fore(i,0,(n)-1)
#define all(x) (x).begin(),(x).end()

template< typename T >
struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}

  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};

template< typename T >
using Edges = vector< edge< T > >;
template< typename T >
using WeightedGraph = vector< Edges< T > >;
using UnWeightedGraph = vector< vector< int > >;
template< typename T >
using Matrix = vector< vector< T > >;

ll d(ll src,ll to,ll x,ll y){
    ll ret=abs(to-src);
    chmin(ret,abs(to-x)+abs(y-src)+1);
    chmin(ret,abs(src-x)+abs(y-to)+1);
    return ret;
}
void solve(long long N, long long X, long long Y){
    vl ans(N);
    rep(i,N)fore(j,i+1,N-1){
        ans[d(i,j,X-1,Y-1)]++;
    }
    fore(i,1,N-1){
        cout<<ans[i]<<endl;
    }
}

int main(){
    long long N;
    scanf("%lld",&N);
    long long X;
    scanf("%lld",&X);
    long long Y;
    scanf("%lld",&Y);
    solve(N, X, Y);
}