ABC160——Task D：Line++ - Problem

Problem5265--ABC160——Task D：Line++

5265: ABC160——Task D：Line++

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Time Limit : 1.000 sec Memory Limit : 256 MiB

Submit Solved: 2 Submit Num: 2 Statistics ShowOff!

Description

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 $(i, j)\ (1 ≤ i < j ≤ N)$
such that the shortest distance between Vertex $i$ and Vertex $j$ in G is $k$.

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.

Constraints

$3 ≤ N ≤ 2×10^3$
$1 ≤ X, Y ≤ N$
$X+1 < Y$
All values in input are integers.

Sample 1 Input

5 2 4

Sample 1 Output

The graph in this input is as follows:

There are five pairs (i,j)(1≤i<j≤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≤i<j≤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≤i<j≤N) such that the shortest distance between Vertex i and Vertex j is 3: (1,5).
There are no pairs (i,j)(1≤i<j≤N) such that the shortest distance between Vertex i and Vertex j is 4.

Sample 2 Input

3 1 3

Sample 2 Output

3
0

The graph in this input is as follows:

Sample 3 Input

7 3 7

Sample 3 Output

HINT

【题目来源】
https://atcoder.jp/contests/abc160/tasks/abc160_d

Source/Category

AtCoder_ABC 100.160.ABC160

5265: ABC160——Task D：Line++

Description

Input

Output

Constraints

Sample 1 Input Copy

Sample 1 Output Copy

Sample 2 Input Copy

Sample 2 Output Copy

Sample 3 Input Copy

Sample 3 Output Copy