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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
long long arr[2003][2003],cnt[2005];
int main()
{
	long long i,j,k,n,m,x,y,z,yy;
	cin>>n>>x>>y;
	for (i=1;i<=n;i++)
	{
		for (j=i+1;j<=n;j++)
		{
			arr[i][j]=j-i;
		}
	}
	z=arr[x][y]-1;
	for (i=1;i<=x;i++)
	{
		for (j=y;j<=n;j++)
		{
			arr[i][j]=arr[i][j]-z;
		}
	}
	for (i=1;i<=x;i++)
	{
		for (j=y-1;j>x;j--)
		{
			yy=arr[i][y]+y-j;
			arr[i][j]=min(yy,arr[i][j]);
		}
	}
	for (i=x;i<y;i++)
	{
		for (j=y;j<=n;j++)
		{
			yy=arr[x][j]+i-x;
			arr[i][j]=min(yy,arr[i][j]);
		}
	}
	for (i=1;i<=n;i++)
	{
		for (j=i+1;j<=n;j++)
		{
			//cout<<arr[i][j]<<" ";
			cnt[arr[i][j]]++;
		}
		//cout<<endl;
	}
	for (i=1;i<n;i++)
	{
		cout<<cnt[i]<<endl;
	}	
}