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 <algorithm>
#include <iostream>
#include <math.h>
#include <stdio.h>
#include <string>
#include <sstream>
#include <vector>
#include <set>
#include <map>
#include <cmath>
#define rep(i, n) for(int i = 0; i < (int)(n); i++)

using namespace std;
int length(int i,int j,int X,int Y){
	return min(j-i, abs(X-i) + 1 + abs(Y - j));
}
int main()
{
	int N, X, Y;
	cin>>N>>X>>Y;
	int *lengthArray = new int[N];
	for(int i = 0 ; i < N; i++){
		lengthArray[i] = 0;
	}
	for(int i = 0; i < N - 1; i++){
		for(int j = i + 1; j < N; j++){
			int L = length(i,j,X-1,Y-1);
			lengthArray[L] +=1;
			//cout<<L<<endl;
		}
	}
	sort(lengthArray,lengthArray + N,greater<int>());
	for(int i = 0 ; i < N-1; i++){
		cout<<lengthArray[i]<<endl;
	}
	return 0;
}