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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io. *;
import java.lang.reflect.Array;
import java.util.*;
import static java.lang.Math.*;
public class Main {

    static int visited[];
    static ArrayList<ArrayList<Integer>> adjlist;
    static class edge implements  Comparator<edge>{
        int dest;
        int cost;

        public edge(int dest, int cost) {
            this.dest = dest;
            this.cost = cost;
        }

        @Override
        public int compare(edge o1, edge o2) {
            return o1.cost-o2.cost;
        }
    }

    static int count[];

    static class Graph{
        int V;
        ArrayList<ArrayList<edge>> adj;
        PriorityQueue<edge> pq;
        int dist[];
        public Graph(int V){
            this.V = V;
            adj = new ArrayList<>(V);
            pq = new PriorityQueue<>(V,new edge(-1,-1));
            dist = new int[V];
            for(int i=0; i<V; i++){
                dist[i] = Integer.MAX_VALUE;
                adj.add(i,new ArrayList<>());
            }
        }

        void addedge(int u, int v, int w ){
            adj.get(u).add(new edge(v,w));
            adj.get(v).add(new edge(u,w));
        }

        void dijkstra(int src){
            for(int i=0; i<V; i++){
                dist[i] = Integer.MAX_VALUE;
            }
            dist[src] = 0;
            pq.add(new edge(src,0));
            while (!pq.isEmpty()){
                int u = pq.poll().dest;
                for(int i=0; i<adj.get(u).size(); i++){
                    int v = adj.get(u).get(i).dest;
                    int w = adj.get(u).get(i).cost;
                    if(dist[u]+w<=dist[v]){
                        dist[v] = dist[u] + w;
                        pq.add(new edge(v,dist[v]));
                    }
                }
            }
            for(int i=1; i<V; i++) {
                count[dist[i]]++;
            }
        }


    }



    static  int I[];
    static  int L[];
    static void LIS(int n, int arr[]){
        I = new int[n+1];
        L = new int[n];
        I[0] = Integer.MIN_VALUE;
        for(int i=1;i<=n; i++){
            I[i] = Integer.MAX_VALUE;
        }
        int lisLength = 1;

        for(int i=n-1; i>=0; i--) {
            int low = 1;
            int high = lisLength;
            int mid = 0;
            while (low < high) {
                mid = (low + high) >> 1;
                if (I[mid] <= arr[i]) {
                    high = mid;
                } else {
                    low = mid + 1;
                }
            }
            I[high] = arr[i];
            L[i] = high;
            if(lisLength<=high){
                lisLength++;
            }
        }
    }

    public static void main(String[] args) {
        FastReader sc = new FastReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = sc.nextInt();
        int x = sc.nextInt();
        int y = sc.nextInt();
        count = new int[n+1];
        Graph gh = new Graph(n+1);
        for(int i=1; i<n; i++){
            gh.addedge(i,i+1,1 );
        }
        gh.addedge(x,y,1);
        for(int i=1; i<=n; i++){
            gh.dijkstra(i);
        }
        for(int i=1; i<n; i++){
            pw.println(count[i]/2);
        }
        pw.close();

    }

    static void debug(Object...obj) {
        System.err.println(Arrays.deepToString(obj));
    }

    static class FastReader {
        InputStream is;
        private byte[] inbuf = new byte[1024];
        private int lenbuf = 0, ptrbuf = 0;

        public FastReader(InputStream is) {
            this.is = is;
        }

        public int readByte(){
            if(lenbuf == -1)throw new InputMismatchException();
            if(ptrbuf >= lenbuf){
                ptrbuf = 0;
                try {
                    lenbuf = is.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if(lenbuf <= 0)
                    return -1;
            }
            return inbuf[ptrbuf++];
        }
        public boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }
        public int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b)) ;
            return b;
        }
        public String next(){
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while(!(isSpaceChar(b))) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public String nextLine(){
            int b = readByte();
            StringBuilder sb = new StringBuilder();
            while(b != '\n' || b != '\r'){
                sb.appendCodePoint(b);
            }
            return sb.toString();
        }
        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }
        public long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
        public char[] next(int n){
            char[] buf = new char[n];
            int b = skip(), p = 0;
            while (p < n && !(isSpaceChar(b))) {
                buf[p++] = (char) b;
                b = readByte();
            }
            return n == p ? buf : Arrays.copyOf(buf, p);
        }
        public char nextChar () {
            return (char) skip();
        }
    }
}