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 (Clang 3.8.0) (judge verdict: Accepted)

// #include <bits/stdc++.h>
#include <iostream>  // cin, cout, string
#include <algorithm> // sort, min/max, upper/lower_bound, transform, count/copy_if
#include <vector>
#include <utility> // pair, swap
#include <functional>
#include <iomanip> // setprecision
#include <map>
#include <set> // multiset
#include <unordered_map>
#include <unordered_set>
#include <tuple>
#include <stack>
#include <queue> // priority_queue
#include <deque>
#include <bitset>
#include <array>
#include <list>
#include <forward_list>
#include <complex>
#include <ratio>
#include <cassert>
#include <numeric> // accumulate, itoa
#include <random>  // mt19937
#include <iterator>
#include <chrono>
#include <cstring>

using namespace std;

// #define int long long

using i64 = int64_t;
using ll = long long;
using ld = long double;

template <typename T>
using vec = vector<T>;
template <typename T>
using mat = vec<vec<T>>;
template <typename T>
using dic = unordered_map<string, T>;
template <typename T>
using pqg = priority_queue<T, vector<T>, greater<T>>; // dijkstra
// template<typename T, typename U> using P = pair<T, U>;
// template<typename... Args> using func = function<Args...>;
// template<typename T> using pq = priority_queue<T>;

using pii = pair<int, int>;
using ppi = pair<pii, int>;
using pip = pair<int, pii>;
using ppp = pair<pii, pii>;

using vi = vec<int>;
using mi = mat<int>; // Graph
using vp = vec<pii>;

constexpr int IINF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
// constexpr int INF = sizeof(int) == sizeof(long long) ? LINF : IINF;
constexpr long long MOD = 1e9 + 7;

#define _overload(_1, _2, _3, name, ...) name
#define _rep1(i, a, b) for (int i = (a), _##i = (b); i < _##i; ++i)
#define _rep2(i, n) _rep1(i, 0, n)
#define _rep3(n) _rep2(i, n)
#define rep(...) _overload(__VA_ARGS__, _rep1, _rep2, _rep3)(__VA_ARGS__)
#define _rrep1(i, a, b) for (int i = (b)-1, _##i = (a); i >= _##i; --i)
#define _rrep2(i, n) _rrep1(i, 0, n)
#define _rrep3(n) _rrep2(i, n)
#define rrep(...) _overload(__VA_ARGS__, _rrep1, _rrep2, _rrep3)(__VA_ARGS__)

#define each(i, a) for (auto &&i : a)
#define each2(i, a) for (const auto &i : a)

#define pb push_back
// emplace_back(*) == push_back(constructor(*))
#define eb emplace_back
#define pob pop_back
#define pf push_front
#define pof pop_front

#define np next_permutation
#define pp prev_permutation

// make_pair(A, B) == pair<T, U>(A, B)
#define mp make_pair
// mt(...) == tie(...)
#define mt make_tuple

#define ft first
#define sd second

#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define sz(a) (int)(a).size()
#define rev(a) reverse(all(a))
#define rs(a, l) (a).resize(l)

#define upper(s) transform(all(s), (s).begin(), topper)
#define lower(s) transform(all(s), (s).begin(), tolower)

#define sum(a) accumulate(all(a), 0)
#define elif else if
#define unless(a) if (!(a))
#define qt(a) #a

#define endl '\n'
#define dec(n) fixed << setprecision(n)
#define zfl(n) setfill(‘0’) << setw(n)

template <typename T = int, T l = 0, T r = (T)MOD>
auto rnd = bind(uniform_int_distribution<T>(l, r), mt19937(chrono::steady_clock::now().time_since_epoch().count()));

template <typename T>
inline constexpr T gcd(T a, T b)
{
    if (a == 0 || b == 0)
        return 0;
    while (b)
    {
        a = a % b;
        swap(a, b);
    }
    return a;
}
template <typename T>
inline constexpr T extgcd2(T a, T b, T &x, T &y)
{
    x = 1;
    y = 0;
    while (b)
    {
        T t = a / b;
        a -= t * b;
        swap(a, b);
        x -= t * y;
        swap(x, y);
    }
    return a;
}
template <typename T>
inline constexpr T lcm(T a, T b) { return a / gcd(a, b) * b; }

template <typename T>
inline constexpr bool chmax(T &a, const T &b)
{
    if (a < b)
    {
        a = b;
        return true;
    }
    return false;
}
template <typename T>
inline constexpr bool chmin(T &a, const T &b)
{
    if (b < a)
    {
        a = b;
        return true;
    }
    return false;
}

template <typename A, typename B>
istream &operator>>(istream &is, pair<A, B> &p)
{
    is >> p.first;
    is >> p.second;
    return is;
}
template <typename A, typename B>
ostream &operator<<(ostream &os, const pair<A, B> &p)
{
    os << p.first << " " << p.second;
    return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v)
{
    for (auto &&x : v)
        is >> x;
    return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v)
{
    for (int i = 0; i < (int)v.size(); ++i)
        cout << v[i] << (i + 1 != (int)v.size() ? " " : "");
    return os;
}

#define debug(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg>
void __f(const char *name, const Arg &arg)
{
    cerr << name << " : " << arg << endl;
}
template <typename Arg, typename... Args>
void __f(const char *names, const Arg &arg, const Args &... args)
{
    const char *comma = strchr(names + 1, ',');
    cerr.write(names, comma - names) << " : " << arg << " | ";
    __f(comma + 1, args...);
}

inline auto yes(const bool &c) { return c ? "yes" : "no"; }
inline auto Yes(const bool &c) { return c ? "Yes" : "No"; }
inline auto YES(const bool &c) { return c ? "YES" : "NO"; }
inline auto Possible(const bool &c) { return c ? "Possible" : "Impossible"; }
inline auto POSSIBLE(const bool &c) { return c ? "POSSIBLE" : "IMPOSSIBLE"; }

constexpr int lim = 100007; // 10^5+7

int n, x, y;

signed main()
{
    cin.tie(0);
    cout.tie(0);
    ios_base::sync_with_stdio(false);
    cin >> n >> x >> y;
    x--;
    y--;
    int ans[3000];
    rep(n)
    {
        rep(j, i + 1, n)
        {

            int d = min((min(abs(j - i), abs(x - i) + abs(j - y) + 1)), abs(y - i) + abs(j - x) + 1);
            ans[d - 1]++;
        }
    }
    rep(n - 1) cout << ans[i] << endl;
    return 0;
}