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)

#define _GLIBCXX_DEBUG//TLEの原因になるので注意！！！！！！！！！！！
#include<cmath>
#include <bits/stdc++.h>
using ll = long long;
using namespace std;
vector<int> arr;
stack<int> st;
queue<int> qu;
queue<pair<int,int> > qu2;
priority_queue<int> pq;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
#define rep2(i,n) for(int i=1; i<=(int)(n); i++)
#define mins(x,y) x=min(x,y)
#define maxs(x,y) x=max(x,y)
typedef set<int> set_t;
typedef set<string> set_g;
typedef complex<double> xy_t;
static const int NIL = -1;
static const int INF = 1000000007;
#define mp make_pair
#define sz(x) int(x.sise())
#define mod 1000000007
#define reps(i,s,n) for(int i = s; i < n; i++)
#define Rreps(i,n,e) for(int i = n - 1; i >= e; --i)
#define Rrep(i,n) Rreps(i,n,0)
deque<int> deq;
#define fi first
#define se second
//#define int long long

//cerrはコメントアウトしなくても通る//ただしTLEを引き起こすことがある

//const ll MOD = 998244353;
const ll MOD = (1e+9) + 7;
//const ll INF = 1LL << 60;
//typedef pair<ll,ll> P;
typedef pair<int, int> P;
bool chmx(int &a, int b) {
	if (b > a) {
		a = b;
		return true;
	}
	return false;
}

bool chmn(int &a, int b) {
	if (b < a) {
		a = b;
		return true;
	}
	return false;
}

vector<int> to[2005];
int dis[2005][2005];
int ans[2005];

int main(){
    int n,x,y;
    cin >> n>> x>>y;
    x--;y--;
    rep(i,n){
        for(int j=i+1;j<n;j++){
            int p=abs(i-x)+abs(j-y)+1;
            if(p<j-i){
                ans[p]++;
            }else{
                ans[j-i]++;
            }
        }
    }
    rep2(i,n-1){
        cout<<ans[i]<<endl;
    }
    return 0;
}