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 Ruby (2.3.3) (judge verdict: Accepted)

n,x,y=gets.split.map &:to_i
as=[0]*(n-1)
1.upto(x-1){|d|
  as[d-1]=x-d
}
1.upto(n-y){|d|
  as[d-1]+=n-y+1-d
}
1.upto(x){|s|
  y.upto(n){|e|
    d=x-s+e-y+1
    as[d-1]+=1
  }
  (x+1).upto(y-1){|e|
    d=[e,x+y+1-e].min-s
    as[d-1]+=1
  }
}
(x+1).upto(y-1){|s|
  y.upto(n){|e|
    d=e-[s,x+y-1-s].max
    as[d-1]+=1
  }
}
(x+1).upto(y-2){|s|
  (s+1).upto(y-1){|e|
    d=[e-s,s-x+y-e+1].min
    as[d-1]+=1
  }
}
puts as