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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

# N=頂点数、X,Y=座標
N, X, Y = map(int, input().split())
X -= 1
Y -= 1

# 未セットの値
INF = 10**4

# キューデータ(次の値、最短距離)
queue_list = []

# 最短距離ごとのリスト
min_e_list = [0 for i in range(N)]

for i in range(N):
    # キューデータ初期値をセット
    queue_list.append([i, 0])
    # 最短距離リスト(最短距離)
    min_dist_list = [INF for i in range(N)] 

    # キューデータが空になるまで繰り返す
    while(len(queue_list) != 0):
        
        # 先頭データを取り出す。
        pop_data = queue_list.pop(0)

        # 取り出した座標がセット済みの場合は何もしない
        if(min_dist_list[pop_data[0]] != INF):
            continue

        # 最短距離リストにデータセット
        min_dist_list[pop_data[0]] = pop_data[1]

        # 2重に数えないよう(i < 取り出した座標時)、最短距離ごとのリストにデータセット
        if(i < pop_data[0]):
            min_e_list[pop_data[1]] += 1

        # 1.隣の頂点(次の座標、+1,-1した値)
        if(pop_data[0]+1 < N):
            queue_list.append([pop_data[0]+1, pop_data[1]+1])
        if(pop_data[0] > 0 and pop_data[0]-1 < N):
            queue_list.append([pop_data[0]-1, pop_data[1]+1])
        
        # 2.X,Yで示した値
        if(pop_data[0] < Y and pop_data[0] == X):
            queue_list.append([Y, pop_data[1]+1])
        if(pop_data[0] < X and pop_data[0] == Y):
            queue_list.append([X, pop_data[1]+1])

# 出力
for i,v in enumerate(min_e_list):
    if(i != 0):
        print(v)