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)

///====================== TEMPLATE STARTS HERE =====================///
#include <bits/stdc++.h>
using namespace std;

//#include <ext/pb_ds/assoc_container.hpp> // Include for built in treap
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;

//#include <sys/resource.h>     // for linux stack memory increase
//#define gc getchar_unlocked   // for linux fast io
//#define gc getchar            // for windows fast io

#define pb push_back
#define MP make_pair
#define ff first
#define ss second
#define nl puts("")
#define sp printf(" ")
#define phl debug("Hello")
#define FOR(i,x,y) for(vlong i = (x) ; i <= (y) ; ++i)
#define ROF(i,x,y) for(vlong i = (y) ; i >= (x) ; --i)
#define CLR(x,y) memset(x,y,sizeof(x))
#define ALL(x) (x).begin(),(x).end()
#define SZ(x) ((vlong)(x).size())
#define UNIQUE(V) (V).erase(unique((V).begin(),(V).end()),(V).end())
#define MIN(a,b) ((a)<(b)?(a):(b))
#define MAX(a,b) ((a)>(b)?(a):(b))
#define ABS(x) ((x)<0?-(x):(x))
#define FABS(x) ((x)+eps<0?-(x):(x))
#define SQ(x) ((x)*(x))
#define LCM(x,y) (((x)/gcd((x),(y)))*(y))
#define POPCOUNT __builtin_popcountll
#define RIGHTMOST __builtin_ctzll
#define LEFTMOST(x) (63-__builtin_clzll((x)))
#define NUMDIGIT(x,y) (((vlong)(log10((x))/log10((y))))+1)
#define NORM(x) if(x>=mod) x-=mod;if(x<0) x+=mod;
#define ODD(x) (((x)&1)==0?(0):(1))
#define Set(N,p) N=((N)|((1LL)<<(p)))
#define Reset(N,p) N=((N)&(~((1LL)<<(p))))
#define Check(N,p) (!(((N)&((1LL)<<(p)))==(0)))
#define fast_cin ios_base::sync_with_stdio(false);cin.tie(NULL)
#define arrayIndexPrint(A,i) cerr<<"~ At pos: "<<i<<" = "<<A[i]
#define dump(x) cerr<<"~ "<<#x<<" = "<<x<<endl
#define arrayPrint(A,st,ed) cerr<<"~ Array:";FOR(i,st,ed) cerr<<" "<<A[i];cerr<<endl
#define LINE cerr<<"\n"; FOR(i,0,50) cerr<<"=";cerr<<"\n\n"

#define LL long long
#define LLU long long unsigned int
typedef long long vlong;
typedef unsigned long long uvlong;
typedef pair < int, int > pii;
typedef pair < vlong, vlong > pll;
typedef vector<int> vi;
typedef vector<vlong> vl;
typedef vector<pll> vll;
//typedef tree <int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> pb_ds;

#ifdef forthright48
     #include <ctime>
     clock_t tStart = clock();
     #define debug(args...) {dbg,args; cerr<<endl;}
     #define timeStamp debug ("Execution Time: ", (double)(clock() - tStart)/CLOCKS_PER_SEC)
     #define bug printf("%d\n",__LINE__);

#else
    #define debug(args...)  // Just strip off all debug tokens
    #define timeStamp
#endif

struct debugger{
    template<typename T> debugger& operator , (const T& v){
        cerr<<v<<" ";
        return *this;
    }
}dbg;

inline vlong gcd ( vlong a, vlong b ) {
    a = ABS ( a ); b = ABS ( b );
    while ( b ) { a = a % b; swap ( a, b ); } return a;
}

#ifdef forthright48
    #define line                    cout << "\n===================\n"
    #define trace(...)              __f( #__VA_ARGS__ , __VA_ARGS__ )
    template <typename Arg1>
    void __f(const char* name, Arg1&& arg1){
        cerr << name << " = " << arg1 << "\n";
    }
    template <typename Arg1, typename... Args>
    void __f(const char* names, Arg1&& arg1, Args&&... args){
        const char* comma = strchr(names + 1, ',');
        cerr.write(names, comma - names) << " = " << arg1 << " , ";
    __f(comma + 1, args...);
    }
#else
    #define line
    #define trace(...)
#endif

vlong ext_gcd ( vlong A, vlong B, vlong *X, vlong *Y ){
    vlong x2, y2, x1, y1, x, y, r2, r1, q, r;
    x2 = 1; y2 = 0;
    x1 = 0; y1 = 1;
    for (r2 = A, r1 = B; r1 != 0; r2 = r1, r1 = r, x2 = x1, y2 = y1, x1 = x, y1 = y ) {
        q = r2 / r1;
        r = r2 % r1;
        x = x2 - (q * x1);
        y = y2 - (q * y1);
    }
    *X = x2; *Y = y2;
    return r2;
}

inline vlong modInv ( vlong a, vlong m ) {
    vlong x, y;
    ext_gcd( a, m, &x, &y );
    x %= m;
    if ( x < 0 ) x += m;
    return x;
}

inline vlong bigmod ( vlong a, vlong p, vlong m ) {
    vlong res = 1 % m, x = a % m;
    while ( p ) {
        if ( p & 1 ) res = ( res * x ) % m;
        x = ( x * x ) % m; p >>= 1; /// For bigmod2 multiply here using mulmod
    }
    return res;
}


//int knightDir[8][2] = { {-2,1},{-1,2},{1,2},{2,1},{2,-1},{-1,-2},{1,-2},{-2,-1} };
//int dir4[4][2] = {{-1,0},{0,1},{1,0},{0,-1}};
//int dir8[8][2] = {{-1,0},{0,1},{1,0},{0,-1},{-1,-1},{1,1},{1,-1},{-1,1}};
const vlong inf = 2147383647;
const vlong mod = 1000000007;
const double pi = 2 * acos ( 0.0 );
const double eps = 1e-11;
//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); /// For generating random numbers

///======================  TEMPLATE ENDS HERE  =====================///

#define SIZE 2005
#define BIG 100000000

int N, X, Y;
vector<int> G[SIZE];    /// Graph
int level[SIZE][SIZE];        /// level of the nodes (distance, as the graph is unweighted)

queue<int> Q;
void BFS(int source) {
    while(!Q.empty()) Q.pop();

    for(int i=0; i<SIZE; i++) level[source][i] = BIG; /// initially the distance is inf (it is also used as visited)

    Q.push(source);     /// push source node in queue
    level[source][source] = 0;  /// level of source node is 0

    while(!Q.empty()) {
        int curr = Q.front();   /// curr node in the front of the queue, pop it
        Q.pop();

        for(int i = 0; i<G[curr].size(); i++) {
            int next = G[curr][i];
            if(level[source][next] == BIG) {    /// if next node is not updated update it
                level[source][next] = level[source][curr] + 1;  /// update level of next node
                Q.push(next);                   /// push next in the queue
            }
        }
    }
    return;
}

int cnt[SIZE];


int main () {
    #ifdef forthright48
    freopen ( "input.txt", "r", stdin );
    //freopen ( "output.txt", "w", stdout );
    #endif // forthright48

    fast_cin;

    cin >> N >> X >> Y;

    for(int i=1; i<=N-1; i++) {
        G[i].push_back(i+1);
        G[i+1].push_back(i);
    }
    G[X].push_back(Y);
    G[Y].push_back(X);

    for(int i=1; i<=N; i++) {
        BFS(i);
    }

    for(int i=1; i<=N-1; i++) {
        for(int j=i+1; j<=N; j++) {
            cnt[level[i][j]]++;
        }
    }

    for(int i=1; i<=N-1; i++) {
        cout << cnt[i] << "\n";
    }

    return 0;
}