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: Wrong Answer)


// Problem : D - Line++
// Contest : AtCoder Beginner Contest 160
// URL : https://atcoder.jp/contests/abc160/tasks/abc160_d
// Memory Limit : 1024.000000 MB 
// Time Limit : 2000.000000 milisec 
// Powered by CP Editor (https://github.com/coder3101/cp-editor2)

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
//#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast","unroll-loops","omit-frame-pointer","inline") //Optimization flags
//#pragma GCC option("arch=native","tune=native","no-zero-upper") //Enable AVX
#pragma GCC target("avx2")  //Enable AVX
#define pb push_back
#define IOS                                                                    \
  ios_base::sync_with_stdio(false);                                            \
  cin.tie(0);                                                                  \
  cout.tie(0);cout<<fixed<<setprecision(16);
#define ll long long int
#define ld long double
#define el '\n'
#define El '\n'
#define PI (ld)3.141592653589793238462643383279502884197169399375105820974944
#define inf (ll)1000000000
#define mod (ll)1000000007
#define mod1 (ll)998244353
#define fo(i, n) for (long long i = 0; i < n; i++)
#define pll pair<ll, ll>
#define ml map<ll,ll>
#define vpl vector<pll>
#define vvl vector<vector<ll> >
#define vvpl vector< vector<pll> >
#define ff first
#define ss second
#define pqueue priority_queue< ll >
#define pdqueue priority_queue< ll,vl ,greater< ll > >
#define mem(a,b) memset(a,b,sizeof(a));
//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define sz(a) (ll)a.size()
#define all(a) a.begin(),a.end()
#define vl vector<ll>


/*#define error(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator<string> _it(_ss); err(_it, args); }

void err(istream_iterator<string> it) {}
template<typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
	cerr << *it << " = " << a << endl;
	err(++it, args...);
}*/


//#define x ff
//#define y ss
#define pt(a) for(auto it:a)cout<<it<<" ";cout<<endl;
unsigned seed = std::chrono::system_clock::now().time_since_epoch().count();
using namespace std;

using namespace __gnu_pbds;
 
typedef tree<pll,null_type,less<pll>,rb_tree_tag,tree_order_statistics_node_update> order_set;

// vector
template<class T> istream& operator >> (istream &is , vector<T> &v) { for(T &a : v) is >> a; return is; }
template<class T> ostream& operator << (ostream &os , const vector<T> &v) { for(const T &t : v) os << t<<" "; return os << endl; }
// pair
template<class T, class U> ostream& operator << (ostream &os , const pair<T, U> &v) { return os << v.first << " " << v.second ; }

double gcd(double a, double b) { return a < 0.01 ? b : gcd(fmod(b, a), a); }

long long bpow(long long a, long long b, long long m) {
  a %= m;
  long long res = 1;
  while (b > 0) {
    if (b & 1)res = res * a % m;
      a = a * a % m;
      b >>= 1;
  }
  return res;
}


ll kv;
ll t,n,x,y,h,k,z,p,q,w;
string s,s1,s2;
//vvl v;
//vl vis,d;

int main() {
    IOS;
    cin>>n>>p>>q;
	vl v(n,0);
	kv=n-(q-p-1);
	z=q-p+1;
	fo(i,n-1){
		v[i+1]=max(0ll,kv-(i+1));
		if(i+1<=z/2)v[i+1]+=z;
		v[i+1]+=max(0ll,min(i,p-1)-max(i-z/2,0ll))*2;
		v[i+1]+=max(0ll,min(i,n-q)-max(i-z/2,0ll))*2;
	}
	v[1]--;
	for(int i=2;i<n;i++){
		if(n-q+1>=i)v[i]--;
		if(p>=i)v[i]--;
	}
	fo(i,n-1){
		cout<<v[i+1]<<el;
	}
    return 0;
}