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)

/*	
*  Sachin Mittal
*/
#include<bits/stdc++.h>
#define int long long
#define M 998244353
#define mod 1000000007
#define all(v) v.begin(),v.end()
#define ios ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define F first
#define S second
#define mem0(dp) memset(dp,0,sizeof(dp))
#define mem1(dp) memset(dp,-1,sizeof(dp))
#define pb push_back
#define fr(i,j,n) for(int i=j;i<n;i++)
#define sz(s) (int)(s.size())
using namespace std;
int32_t main(){
ios
int t=1;
//cin>>t;
while(t--)
{
	int n,x,y;
	cin>>n>>x>>y;
	vector<int> ans(n+1,0);
	for(int i=1;i<n;i++)
	{
		for(int j=i+1;j<=n;j++)
		{
			if(i<x)
			{
				if(j<=x)
					ans[j-i]++;
				else if(j<=y)
				{
					ans[min(j-i,x-i+1+y-j)]++;
				}
				else ans[x-i+1+j-y]++;
			}
			else if(i<y)
			{
				ans[min(j-i,i-x+1+abs(j-y))]++;
			}
			else ans[j-i]++;
		}
	}
	for(int i=1;i<n;i++)
		cout<<ans[i]<<'\n';	
}
}