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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Map;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Main {

	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskX solver = new TaskX();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskX {
		public void solve(int testNumber, InputReader in, PrintWriter out) {

			int n = in.nextInt();
			int a = in.nextInt();
			int b = in.nextInt();
			long[] an = new long[n];
			for (int i = 0; i < n; i++) {
				an[i] = in.nextLong();
			}

			Arrays.sort(an);

			boolean isAllEqual = (an[0] == an[n-1]);

			double as = 0;
			for (int i = 0; i < a; i++) {
				as += an[n-i-1];
			}
			as /= a;

			int minAInACount = 0;
			int minAInALLCount = 0;
			for (int i = n-a; i < n; i++) {
				if (an[n-a] == an[i]) minAInACount++;
			}
			for (int i = 0; i < n; i++) {
				if (an[n-a] == an[i]) minAInALLCount++;
			}

			long ans = 0;
			if (isAllEqual) {
				for (int i = a; i <= b; i++) {
					ans += countCombination(b, i);
				}
			} else {
				ans += countCombination(minAInALLCount, minAInACount);
			}

			out.println(String.format("%1$.6f", as));
			out.println(ans);


		}
	}

	static long countCombination(long n, long r) {
		r = Math.min(r, n-r);
		BigInteger numerator = new BigInteger("1");
		BigInteger donominator = new BigInteger("1");

		for (long i = n; i > n-r; i--) {
			BigInteger is = new BigInteger(String.valueOf(i));
			numerator = numerator.multiply(is);
		}
		for (long i = 1; i <= r; i++) {
			BigInteger is = new BigInteger(String.valueOf(i));
			donominator = donominator.multiply(is);
		}
		return numerator.divide(donominator).longValue();
	}

	static class ArrayUtils {
		public static Map<Integer, Integer> getCountMap(int[] array) {
			Map<Integer, Integer> map = new TreeMap<>();
			for (int x : array)
				map.merge(x, 1, Integer::sum);
			return map;
		}
	}

	static class InputReader {
		BufferedReader in;
		StringTokenizer tok;

		public String nextString() {
			while (!tok.hasMoreTokens()) {
				try {
					tok = new StringTokenizer(in.readLine(), " ");
				} catch (IOException e) {
					throw new InputMismatchException();
				}
			}
			return tok.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(nextString());
		}

		public long nextLong() {
			return Long.parseLong(nextString());
		}

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

		public long[] nextLongArray(int n) {
			long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public InputReader(InputStream inputStream) {
			in = new BufferedReader(new InputStreamReader(inputStream));
			tok = new StringTokenizer("");
		}

	}

}