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 int ll;
const ll mod=998244353;

#define pb push_back
#define mp make_pair


int main() {
    
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);

    ll t,n,x,y;
    cin>>n>>x>>y;
    ll k=n-y+x+1,a[10000];
    for(ll i=1;i<n;i++){
        a[i]=max(0LL,k-1);
        k--;
    }
    for(ll i=x+1;i<y;i++){
        for(ll j=1;j<x;j++){
            ll s=min(i-j,x-j+1+y-i);
            a[s]++;
        }
        for(ll j=y+1;j<=n;j++){
            ll s=min(j-i,i-x+1+j-y);
            a[s]++;
        }
    }
    for(ll i=x;i<=y;i++){
        for(ll j=i+1;j<=y;j++){
            if(i==x && j==y)
                continue;
            ll s=min(j-i,i-x+y-j+1);
            a[s]++;
        }
    }
    for(ll i=1;i<n;i++)
        cout<<a[i]<<"\n";

    return 0;
}