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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
	N,X,Y,loop,k,ans,z,t:Longint;
begin
	read(N,X,Y);
	loop:=Y-X+1;
	for k:=1 to N-1 do begin
		ans:=0;
		if X<k then z:=X-1 else z:=k-1;
		if k-z<=loop div 2 then begin
			if 2*k-loop-1>0 then t:=2*k-loop-1 else t:=0;
			inc(ans,(z-t div 2)*2);
			if(loop mod 2=0)and(loop div 2<k)and(k-loop div 2<X)then dec(ans);
		end;
		if N-Y<k-1 then z:=N-Y else z:=k-1;
		if k-z<=loop div 2 then begin
			if 2*k-loop-1>0 then t:=2*k-loop-1 else t:=0;
			inc(ans,(z-t div 2)*2);
			if(loop mod 2=0)and(loop div 2<k)and(k-loop div 2<N+1-Y)then dec(ans);
		end;
		if N+1+X-Y>k then inc(ans,N+1+X-Y-k);
		if k=1 then dec(ans)else begin
			if X-1>=k-1 then dec(ans);
			if N-Y>=k-1 then dec(ans);
		end;
		if k*2<loop then begin
			inc(ans,loop);
		end else if k*2=loop then begin
			inc(ans,loop div 2);
		end;
		writeln(ans);
	end;
end.