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 m[2001][2001];
int d[2001][2001];
int head,tail;
int n;

int queue[2001];

void solve(int s){
  int i;
  int u;
  int j;
  int v[2001];

  for(i = 0;i < 2001;i++) v[i] = 0;

  head = tail = 0;
  queue[tail++] = s;
  d[s][s] = 0;
  v[s] = 1;

  while(head != tail){
    u = queue[head++];
    for(j = u;j <= n;j++){
      if(m[u][j] == 1){

        if(v[j] == 0){
          queue[tail++] = j;
          v[j] = 1;
        }

        d[u][j] = 1;
        if(d[s][j] > (d[s][u] + 1))
        d[s][j] = d[s][u] + d[u][j];
      }
    }
  }
}

int main(){
  int x,y;
  int i,j,k;
  int cnt;

  scanf("%d %d %d", &n, &x, &y);

  for(i = 0;i < 2001;i++){
    for(j = 0;j < 2001;j++){
      m[i][j] = 0;
      d[i][j] = 9999;
    }
  }

  for(i = 1;i < n;i++) m[i][i + 1] = 1;

  m[x][y] = 1;

  for(i = 1;i < n;i++){
    solve(i);
  }

  for(k = 1;k < n;k++){
    cnt = 0;
    for(i = 1;i < n;i++){
      for(j = i + 1;j <= n;j++){
        if(d[i][j] == k) cnt++;
      }
    }

    printf("%d\n", cnt);
  }

  return 0;
}