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: Runtime Error)


//--------O&Oo&oO&O---------------

#include<bits/stdc++.h>
#define FAST_IO ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
using namespace std;

using in=long long int;

void SOLVE()
{
	#ifndef ONLINE_JUDGE
        freopen("inputf.txt", "r", stdin);
        freopen("outpuf3.txt", "w", stdout);
    #endif
   int n,x,y;
   cin>>n>>x>>y;
   map<int,int> MPP;
   int dis[n+1]={0};
  // dis[1]=0;
   for(int i=2;i<=n;i++)
   {
   		dis[i]=1+dis[i-1];
   		//MPP[dis[i]]++;
   		//cout<<dis[i]<<" ";
   }
   

   dis[y]=dis[x]+1;
   for(int i=y+1;i<=n;i++)
   	dis[i]=dis[i-1]+1;


  
  
   for(int i=2;i<=n;i++)
   {
   	for(int j=1;j<=i-1;j++)
   	{
   		
   			MPP[min(abs(x-j)+1+abs(i-y),min(abs(i-j),abs(y-i)+abs(j-x)+1))]++;
   		
   	}
   }
   for(int i=1;i<=n;i++)
   {
   	cout<<MPP[i]<<"\n";
   	
   }





}

int main()
{
	FAST_IO
	
	SOLVE();

	return 0;
}