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>
#include <vector> 
# include <cstdint>
#define FOR(i,l,r) for(int i=(l);i<(r);++i)
#define RFOR(i,l,r) for(int i=(l);i>=(int)(r);i--)
#define rep(i,n)  FOR(i,0,n)
#define rrep(i,n)  RFOR(i,n-1,0)

// #define int long long
using namespace std;
const int MX = 1e6;
const int inf = 1e9;

using P = pair<int, int>;


vector<int> to[100005];
int cost[100005];
signed main(){
    int n, x, y;
    cin >> n >> x >> y;
    x--; y--;
    rep(i,n) {
        FOR(j, i+1, n) {
            int a = j-i;
            if(x<j || i <y) a = min(a, abs(x-i)+1+abs(y-j));
            cost[a]++;  
            //cout << i+1<<" "<<j+1<<" "<<a << endl; 
        }
    }
    FOR(i,1,n) cout << cost[i] << endl;

    return 0;
}