Problem:
Score : 400 points

Problem Statement

You are given N items.

The value of the i-th item (1 \leq i \leq N) is v_i.

Your have to select at least A and at most B of these items.

Under this condition, find the maximum possible arithmetic mean of the values of selected items.

Additionally, find the number of ways to select items so that the mean of the values of selected items is maximized.

Constraints

1 \leq N \leq 50

1 \leq A,B \leq N

1 \leq v_i \leq 10^{15}

Each v_i is an integer.

Input

The input is given from Standard Input in the following format:

N A B
v_1
v_2
...
v_N

Output

Print two lines.

The first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.

The second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.

Sample Input 1

5 2 2
1 2 3 4 5

Sample Output 1

4.500000
1

The mean of the values of selected items will be maximized when selecting the fourth and fifth items. Hence, the first line of the output should contain 4.5.

There is no other way to select items so that the mean of the values will be 4.5, and thus the second line of the output should contain 1.

Sample Input 2

4 2 3
10 20 10 10

Sample Output 2

15.000000
3

There can be multiple ways to select items so that the mean of the values will be maximized.

Sample Input 3

5 1 5
1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996

Sample Output 3

1000000000000000.000000
1

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

public class Main {

    public static InputReader in;
    public static PrintWriter out;
    
    public static final int MOD = (int) (1e9 + 7);
    public static void main(String[] args) {
        in = new InputReader(System.in);
        out = new PrintWriter(System.out);
        
        int N = in.nextInt();
        int A = in.nextInt(), B = in.nextInt();
        
        Long[] v = new Long[N];
        for (int i = 0; i < N; i++) {
	    v[i] = in.nextLong();
	}
        Arrays.sort(v, Collections.reverseOrder());
        
        double[] sum = new double[N + 1];
        for (int i = 1; i <= N; i++) {
	    sum[i] += sum[i - 1] + v[i - 1];
	}
        int maxMeanIdx = 0;
        double maxValue = 0;
        for(int i = A; i <= B; i++) {
            if(sum[i]/(1.0*i) > maxValue) {
        	maxValue = sum[i]/(1.0*i);
        	maxMeanIdx = i;
            }
        }
        
        HashSet<Integer> sizes = new HashSet<Integer>();
        for (int i = A; i <= B; i++) {
	    if(sum[i]*maxMeanIdx == sum[maxMeanIdx]*i) {
		sizes.add(i);
	    }
	}
        
        choose(N, N);
        
        long result = 0;
        for(Integer ii : sizes) {
            long val = v[ii - 1];
            int r = 0, n = 0;
            for(int i = 0; i < ii; i++) {
                if(v[i] == val) {
                    n++;
                    r++;
                }
            }
            for(int i = ii; i < N; i++) {
                if(v[i] == val) {
                    n++;
                }
            }
            result += nCr[n][r];
        }
        
        out.printf("%f\n", maxValue);
        out.println(result);
        
        out.close();
    }
    
    public static long[][] nCr;
    public static void choose(int maxN, int maxR) {
	
	nCr = new long[maxN + 1][maxR + 1];
        for (int i = 0; i <= maxN; i++) {
            for (int j = 0; j <= i; j++) {
                if (j == 0 || j == i || i==0) {
                    nCr[i][j] = 1;
                } else {
                    nCr[i][j] = nCr[i-1][j-1] + nCr[i-1][j];
                }
            }
        }
    }
    
    static class Node implements Comparable<Node>{
        int next;
        long dist;
        
        public Node (int u, int v) {
            this.next = u;
            this.dist = v;
        }
        
        public void print() {
            out.println(next + " " + dist + " ");
        }
        
        public int compareTo(Node n) {
            return Integer.compare(-this.next, -n.next);
        }
    }
    
    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public String readString() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
}