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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

module Main where

import           Debug.Trace

data Section = Load1 | Load2 | Load3
main :: IO [()]
main = do
    [n, vertexX, vertexY] <- map read . words <$> getLine

    let numList  = [1 .. n]
    let combList = comb 2 numList

    let shortestList =
            foldl (\acc x -> acc ++ [(aaaa x vertexX vertexY)]) [] combList
    let aaaList = map
            (\x -> do
                sumShortest shortestList x
            )
            (init numList)

    mapM putStrLn (map  (\x->show x)  aaaList)


aaaa :: [Int] -> Int -> Int -> ((Int, Int), Int)
aaaa x vertexX vertexY  = ((start, end), smaller (abs (start-vertexX) + 1 + abs (end-vertexY)) (end - start))
  where
    start    = head x :: Int
    end      = last x :: Int
    pattern1 = ((start <= vertexX) && (end >= vertexY))
    pattern2 = ((start > vertexX) && (end > vertexY) && (start < vertexY))
    pattern3 = ((start < vertexX) && (end < vertexY)) && (end > vertexX)

    pattern4 = ((start >= vertexX) && (end <= vertexY))
    smaller a b = if a < b then a else b



sumShortest :: [((Int, Int), Int)] -> Int -> Int
sumShortest shortestList x =
    foldl (\acc y -> if ((snd y) == x) then (acc + 1) else acc) 0 shortestList

comb :: Int -> [a] -> [[a]]
comb 0 xs       = [[]]
comb _ []       = []
comb n (x : xs) = [ x : y | y <- comb (n - 1) xs ] ++ comb n xs