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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>

int count(int ver_num, int X, int Y, int k)
{
  int cnt = 0;
  int i, j, l, short_num;
  
  for(i = 0; i < ver_num - k; i++)
  {
    short_num = 1 + ver_num - Y;
    cnt++;
    
    for(j = 1; j <= k - 1; j++)
    {
      if((i + j) == X)
      {
        l = short_num - j;
        if(l > 0)
          cnt++;
      }
    }
   
    if(i == X)
    {
      l = short_num - k;
      if(l > 0)
          cnt++;
    }
  }
  
  return cnt;
}

int main()
{
  int ver_num, X, Y;
  int i, n;
  
  scanf("%d %d %d", &ver_num, &X, &Y);
  
  for(i = 1; i < ver_num - 1; i++)
  {
    n = count(ver_num, X, Y, i);
    printf("%d\n", n);
  }
}