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: Wrong Answer)

import sys,math
sys.setrecursionlimit(10**9)
from collections import defaultdict
 
IA = lambda: map(int,input().split())
IAS= lambda: map(str,input().split())


n,x,y=IA()
ans=[0 for i in range(0,n)]


def out():
    for i in range(1,n):
        print(ans[i])
    print()
if x==y:
    for i in range(1,n+1):
        ans[i]=n-i
else:

    m=x+n-y+1

    for i in range(1,m+1):
        ans[i]=m-i
        
    cha=y-x-1
    for i in range(1,cha+1):
        ans[i]+=cha-i
    #out()
    tt=cha//2+1

    def f(tt,x,t=0):
        if tt==1 and x==1:
            ans[1+t]+=1
        add=0
        for i in range(1+t,max(tt,x)+t):
            
            if i<=min(x,tt)+t:
                add+=1
            #print(str(i)+" "+str(add))
            ans[i]+=add
        add=min(x,tt)
        for i in range(max(tt,x)+t,max(tt,x)+min(x,tt)+t):
            #print(str(i)+":"+str(add))
            ans[i]+=add
            add-=1
    if cha%2==1:
        f(tt,x)
        #out()
        f(tt-1,n-y+1,1)
        #out()
        f(tt,n-y+1)
        #out()
        f(tt-1,x,1)

        
    else:
        f(tt-1,x)
        #out()
        f(tt-1,n-y+1,1)
        #out()
        
        f(tt-1,n-y+1)
        #out()
        f(tt-1,x,1)
for i in range(1,n):
    print(ans[i])