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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

public static partial class Program
{
    public static void Main()
    {
        var nab = CRL().ArrayInts();
        var n = nab[0];
        var a = nab[1];
        var b = nab[2];
        var vis = CRL().ArrayLongs().Sort().Reverse().ToArray();

        var maxAve = vis.Take(a).Average();
        CWL(maxAve);

        var count = 0;
        for (int i = a; i <= b; i++)
        {
            var comb = vis.Comb(i);
            count += comb.Count(x => x.Average() == maxAve);
        }

        CWL(count);
    }
}

public static partial class Program
{
    //テンプレここから
    public static int ToInt(this string str) => int.Parse(str);
    public static long ToLong(this string str) => long.Parse(str);
    public static long[] ToLong(this IEnumerable<string> strs) => strs.Select(x => x.ToLong()).ToArray();
    public static int[] ToInt(this IEnumerable<string> strs) => strs.Select(x => x.ToInt()).ToArray();
    public static long[] ArrayLongs(this string str, char opr = ' ') => str.Split(opr).ToLong();
    public static int[] ArrayInts(this string str, char opr = ' ') => str.Split(opr).ToInt();
    public static string CRL() => Console.ReadLine();
    public static void CWL(object obj) => Console.WriteLine(obj);
    public static long Diff(long a, long b) => Math.Abs(Math.Max(a, b) - Math.Min(a, b));
    public static long Sign(this long i) => Math.Sign(i);
    public static bool IsEven(this long i) => i % 2 == 0;
    public static bool IsEven(this int i) => i % 2 == 0;
    public static long[] dx = new long[] {0, -1, 0, 1};
    public static long[] dy = new long[] {-1, 0, 1, 0};
    public static long mod = 1000000007;
    public static string alphabet = "abcdefghijklmnopqrstuvwxyz";
    public static long ToLong(this char c) => c.ToString().ToInt();

    public static long[] Sort(this long[] array)
    {
        var list = array.ToList();
        list.Sort();
        return list.ToArray();
    }

    public static int[] Sort(this int[] array)
    {
        var list = array.ToList();
        list.Sort();
        return list.ToArray();
    }

    public static long GCD(long a, long b) => b == 0 ? a : GCD(b, a % b);

    public static long LCM(long a, long b) => a * b / GCD(a, b);

    public static IEnumerable<IEnumerable<T>> Comb<T>(this IEnumerable<T> items, int r)
    {
        if (r == 0)
        {
            yield return Enumerable.Empty<T>();
        }
        else
        {
            var i = 1;
            foreach (var x in items)
            {
                var xs = items.Skip(i);
                foreach (var c in Comb(xs, r - 1))
                    yield return c.Before(x);

                i++;
            }
        }
    }

    public static IEnumerable<T> Before<T>(this IEnumerable<T> items, T first)
    {
        yield return first;

        foreach (var i in items)
            yield return i;
    }

    //テンプレここまで
}