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: Runtime Error)

#include<stdio.h>
#include<stdlib.h>

#define N 2000
#define M 9999

int a[N + 1][N + 1];
int v[N + 1];
int d[N + 1][N + 1];
int queue[N + 1];
int cnt[N + 1];
int head;
int tail;
int n;

void bfs(int s){
  int u;
  int i;

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

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

  while(head != tail){
    u = queue[head++];
    for(i = 1;i <= n;i++){
      if(a[u][i] == 1 && v[i] == 0){
        queue[tail++] = i;
        d[u][i] = 1;
        v[i] = 1;

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

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

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

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

  for(i = 1;i < n;i++){
    a[i][i + 1] = 1;
    a[i + 1][i] = 1;
  }

  a[x][y] = a[y][x] = 1;

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

    head = 0; tail = 0;
    bfs(i);
  }

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

  for(i = 1;i < n;i++) printf("%d\n", cnt[i]);

  return 0;
}