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 (2.4.0) (judge verdict: Accepted)

# ANSHUL GAUTAM
# IIIT-D

from math import *
from copy import *
from string import *				# alpha = ascii_lowercase
from random import *				# l.sort(key=lambda l1:l1[0]-l1[1]) => ex: sort on the basis difference
from bisect import *				# bisect_left(arr,x,start,end)  => start and end parameters are temporary
from sys import stdin				# bisect_left return leftmost position where x should be inserted to keep sorted
from sys import maxsize
from operator import *				# d = sorted(d.items(), key=itemgetter(1))
from itertools import *
from collections import Counter		# d = dict(Counter(l))
from collections import defaultdict # d = defaultdict(list)

'''
5 2 4
'''

def solve(n,x,y):
	adj = [[] for i in range(n+1)]
	adj[x].append(y)
	adj[y].append(x)
	for i in range(1,n):
		adj[i].append(i+1)
		adj[i+1].append(i)
	# print(adj)
	ans = []
	d = {}
	for i in range(1,n):
		d[i] = 0
	for k in range(1,n+1):
		q = [k]
		dis = [maxsize]*(n+1)
		dis[k] = 0
		while(q):
			src = q.pop()
			for nn in adj[src]:
				# if(nn > k or nn == X or nn == Y):
				if(dis[nn] > dis[src]+1):
					# if(src == 4):
						# print('src:',src,'nn:',nn)
					dis[nn] = dis[src] + 1
					q.append(nn)
				# else:
				# 	dis[nn] = 
			# if(k == 3):
			# 	print('src:',src)
			# 	print('dis:',dis)
		curr = 0
		# if(k == 3):
		# print('k:',k,dis)
		for ii in range(k+1,n+1):
			d[dis[ii]] += 1
	return d

N,X,Y = list(map(int, stdin.readline().rstrip().split()))
ans = solve(N,X,Y)
for i in range(1,N):
	print(ans[i])