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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#ifdef BUILT_LOCAL

#include "niklib.h"

#endif

#include <iostream>
#include <utility>
#include <numeric>
#include <vector>
#include <stack>
#include <queue>
#include <algorithm>
#include <string>
#include <cstdio>
#include <cstring>
#include <map>
#include <cmath>
#include <set>
#include <list>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
constexpr ll mod = 1000000007;

typedef long long num;

#define bs(n) (1ll<<(ll)(n))
#define rep(i, n) for(ll (i) = 0;(i) < (n);(i)++)
#define rrep(i, n) for(ll (i) = 1;(i) <= (n);(i)++)

int main() {
    int N, X, Y;
    cin >> N >> X >> Y;
    auto dist = [&N, &X, &Y](int a, int b) {
        int d1 = abs(a - b);
        int d2 = abs(a - X) + abs(b - Y) + 1;
        int d3 = abs(a - Y) + abs(b - X) + 1;
        return min(d1, min(d2, d3));
    };
    int *r = new int[N];
    memset(r, 0, sizeof(int[N]));
    for (int i = 1; i <= N; i++)
        for (int j = i + 1; j <= N; j++) {
            int d = dist(i, j);
            r[d]++;
        }
    for (int i = 1; i < N; i++) cout << r[i] << endl;
}