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 PyPy3 (7.3.0) (judge verdict: Accepted)

#

import sys
input=sys.stdin.readline
from collections import deque

def main():
    N,X,Y=map(int,input().split())
    X-=1
    Y-=1
    adj=[[] for i in range(N)]
    adj[X].append(Y)
    adj[Y].append(X)
    for i in range(N-1):
        adj[i].append(i+1)
        adj[i+1].append(i)
    cnt=[0]*(N)
    for i in range(N):
        dist=[-1]*N
        qu=deque([i])
        dist[i]=0
        while(len(qu)>0):
            v=qu.popleft()
            for nv in adj[v]:
                if dist[nv]==-1:
                    dist[nv]=dist[v]+1
                    cnt[dist[nv]]+=1
                    qu.append(nv)
    for i in range(1,N):
        print(cnt[i]//2)
    
    
if __name__=="__main__":
    main()