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)

#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;
#define ll long long
//increase stack size
#pragma comment(linker, "/STACK:16777216")

ll mxm() {return LLONG_MIN;}
template<typename... Args>
ll mxm(ll a, Args... args) { return max(a,mxm(args...)); }

ll mnm() {return LLONG_MAX;}
template<typename... Args>
ll mnm(ll a, Args... args) { return min(a,mnm(args...)); }

template<class T> ostream& operator<<(ostream& os,vector<T> V){
	os<<"[ ";for(auto v:V)os<<v<<" ";return os<<"]";
}
template<class L,class R> ostream& operator<<(ostream& os,pair<L,R> P){
	return os<<"("<<P.first<<","<<P.second<<")";
}

#define TRACE
#ifdef TRACE
#define trace(...) __f(#__VA_ARGS__,__VA_ARGS__)
template<typename Arg1>
void __f(const char* name,Arg1&& arg1){
	cout<<name<<" : "<<arg1<<endl;
}
template <typename Arg1,typename... Args>
void __f(const char* names,Arg1&& arg1,Args&&... args){
	const char* comma=strchr(names+1,',');cout.write(names,comma-names)<<" : "<<arg1<<" | ";__f(comma+1,args...);
}
#else
#define trace(...) 1
#endif

#define ld long double
#define pll pair<ll,ll>
#define ii pair<int,int>
#define vll vector<ll>
#define vii vector<ii>
#define vi vector<int>
#define vpll vector<pll>
#define vld vector<ld>
#define vvld vector<vld>
#define vvi vector<vi>
#define vvll vector<vll>
#define vvpll vector<vpll>
#define vvii vector<vii>
#define I insert
#define F first
#define S second
#define pb push_back
#define endl "\n"
#define all(x)	x.begin(),x.end()

const int mod=1e9+7;
// 128 bit: __int128
inline int add(int a,int b){a+=b;if(a>=mod)a-=mod;return a;}
inline int sub(int a,int b){a-=b;if(a<0)a+=mod;return a;}
inline int mul(int a,int b){return (a*1ll*b)%mod;}
inline int power(int a,int b){int rt=1;while(b>0){if(b&1)rt=mul(rt,a);a=mul(a,a);b>>=1;}return rt;}
inline int inv(int a){return power(a,mod-2);}

struct compare{
	bool operator() (const int &a,const int &b) const{
		return a>b;
	}
};

const int N = 2e3 + 10;
vvi dist(N, vi(N));

int main()
{
	ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);cout<<setprecision(25);
	int n;
	cin >> n;
	vvi dist(n, vi(n));
	int x, y;
	cin >> x >> y;
	--x, --y;
	vi ans(n);
	for(int i = 0; i < n; i++){
		for(int j = i + 1; j < n; j++){
			dist[i][j] = j - i;
			dist[i][j] = min(dist[i][j], 1 + abs(x - i) + abs(y - j));
			dist[i][j] = min(dist[i][j], 1 + abs(y - i) + abs(x - j));
			ans[dist[i][j]]++;
		}
	}
	for(int i = 1; i <= n - 1; i++)
		cout << ans[i] << endl;
}