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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"errors"
	"fmt"
	"math"
	"os"
	"sort"
	"strconv"
	"strings"
)

/*
var rdr = bufio.NewReaderSize(os.Stdin, 1000000)
// readLine can read long line string (at least 10^5)
func readLine() string {
	buf := make([]byte, 0, 1000000)
	for {
		l, p, e := rdr.ReadLine()
		if e != nil {
			panic(e)
		}
		buf = append(buf, l...)
		if !p {
			break
		}
	}
	return string(buf)
}
// NextLine reads a line text from stdin, and then returns its string.
func NextLine() string {
	return readLine()
}
*/

var sc = bufio.NewScanner(os.Stdin)

// NextLine reads a line text from stdin, and then returns its string.
func NextLine() string {
	sc.Scan()
	return sc.Text()
}

// NextIntsLine reads a line text, that consists of **ONLY INTEGERS DELIMITED BY SPACES**, from stdin.
// And then returns intergers slice.
func NextIntsLine() []int {
	ints := []int{}
	intsStr := NextLine()
	tmp := strings.Split(intsStr, " ")
	for _, s := range tmp {
		integer, _ := strconv.Atoi(s)
		ints = append(ints, integer)
	}
	return ints
}

// NextStringsLine reads a line text, that consists of **STRINGS DELIMITED BY SPACES**, from stdin.
// And then returns strings slice.
func NextStringsLine() []string {
	str := NextLine()
	return strings.Split(str, " ")
}

// NextRunesLine reads a line text, that consists of **ONLY CHARACTERS ARRANGED CONTINUOUSLY**, from stdin.
// Ant then returns runes slice.
func NextRunesLine() []rune {
	return []rune(NextLine())
}

// Max returns the max integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Max(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m < integer {
			m = integer
		}
	}
	return m
}

// Min returns the min integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Min(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m > integer {
			m = integer
		}
	}
	return m
}

// PowInt is integer version of math.Pow
func PowInt(a, e int) int {
	if a < 0 || e < 0 {
		panic(errors.New("[argument error]: PowInt does not accept negative integers"))
	}
	fa := float64(a)
	fe := float64(e)
	fanswer := math.Pow(fa, fe)
	return int(fanswer)
}

// AbsInt is integer version of math.Abs
func AbsInt(a int) int {
	fa := float64(a)
	fanswer := math.Abs(fa)
	return int(fanswer)
}

// DeleteElement returns a *NEW* slice, that have the same and minimum length and capacity.
// DeleteElement makes a new slice by using easy slice literal.
func DeleteElement(s []int, i int) []int {
	if i < 0 || len(s) <= i {
		panic(errors.New("[index error]"))
	}
	// appendのみの実装
	n := make([]int, 0, len(s)-1)
	n = append(n, s[:i]...)
	n = append(n, s[i+1:]...)
	return n
}

// Concat returns a *NEW* slice, that have the same and minimum length and capacity.
func Concat(s, t []rune) []rune {
	n := make([]rune, 0, len(s)+len(t))
	n = append(n, s...)
	n = append(n, t...)
	return n
}

// UpperRune is rune version of `strings.ToUpper()`.
func UpperRune(r rune) rune {
	str := strings.ToUpper(string(r))
	return []rune(str)[0]
}

// LowerRune is rune version of `strings.ToLower()`.
func LowerRune(r rune) rune {
	str := strings.ToLower(string(r))
	return []rune(str)[0]
}

// ToggleRune returns a upper case if an input is a lower case, v.v.
func ToggleRune(r rune) rune {
	var str string
	if 'a' <= r && r <= 'z' {
		str = strings.ToUpper(string(r))
	} else if 'A' <= r && r <= 'Z' {
		str = strings.ToLower(string(r))
	} else {
		str = string(r)
	}
	return []rune(str)[0]
}

// ToggleString iteratively calls ToggleRune, and returns the toggled string.
func ToggleString(s string) string {
	inputRunes := []rune(s)
	outputRunes := make([]rune, 0, len(inputRunes))
	for _, r := range inputRunes {
		outputRunes = append(outputRunes, ToggleRune(r))
	}
	return string(outputRunes)
}

// Strtoi is a wrapper of `strconv.Atoi()`.
// If `strconv.Atoi()` returns an error, Strtoi calls panic.
func Strtoi(s string) int {
	if i, err := strconv.Atoi(s); err != nil {
		panic(errors.New("[argument error]: Strtoi only accepts integer string"))
	} else {
		return i
	}
}

// sort package (snippets)
//sort.Sort(sort.IntSlice(s))
//sort.Sort(sort.Reverse(sort.IntSlice(s)))
//sort.Sort(sort.Float64Slice(s))
//sort.Sort(sort.StringSlice(s))

// copy function
//a = []int{0, 1, 2}
//b = make([]int, len(a))
//copy(b, a)

/*******************************************************************/

var n, a, b int
var V []int
var C [51][51]int

func combination(n int) {
	for i := 0; i <= n; i++ {
		for j := 0; j <= i; j++ {
			if j == 0 || j == i {
				C[i][j] = 1
			} else {
				C[i][j] = C[i-1][j-1] + C[i-1][j]
			}
		}
	}
}

func main() {
	tmp := NextIntsLine()
	n, a, b = tmp[0], tmp[1], tmp[2]
	V = NextIntsLine()
	sort.Sort(sort.Reverse(sort.IntSlice(V)))
	combination(n)

	average := 0.0
	memo := make(map[int]int)
	for i := 0; i < a; i++ {
		average += float64(V[i])
		memo[V[i]]++
	}
	average /= float64(a)

	// 最大の平均を作る数のうち、最小のものの個数を求める
	minimum, maximum := math.MaxInt64, -1
	for k := range memo {
		minimum = Min(minimum, k)
		maximum = Max(maximum, k)
	}
	fmt.Println(maximum, minimum)

	patterns := 0
	x := 0
	for _, v := range V {
		if v == minimum {
			x++
		}
	}
	if minimum != maximum {
		y := memo[minimum]
		patterns = C[x][y]
	} else {
		ub := Min(b, x)
		for i := a; i <= ub; i++ {
			patterns += C[x][i]
		}
	}

	fmt.Println(average)
	fmt.Println(patterns)
}