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;

const int maxn = 2e3+2;

int a[maxn];
int t;
int dis[maxn][maxn];
int main()
{
	ios::sync_with_stdio(0);
	int n,x,y; cin>>n>>x>>y;
	memset(a,0,sizeof a);
	for(int i=1;i<=n;++i)
	{
		for(int j=i+1;j<=n;++j)
		{
			dis[i][j] = j-i;
		}
	}
	for(int i=1;i<=n;++i)
	{
		for(int j=i+1;j<=n;++j)
		{
			dis[i][j] = min(dis[i][j],abs(x-i)+abs(j-y)+1) ;
		}
	}
	for(int i=1;i<=n;++i)
	{
		for(int j=i+1;j<=n;++j)
		{
			++a[dis[i][j]];

		}
	}
	for(int i=1;i<=n-1;++i) cout<<a[i]<<"\n"; 
}