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 {

	private static Scanner sc;
	private static Printer pr;

	private static void solve() {
		int n = sc.nextInt();
		int a = sc.nextInt();
		int b = sc.nextInt();

		long[] v = new long[n];
		Map<Long, Integer> hm = new HashMap<>();
		for (int i = 0; i < n; i++) {
			v[i] = sc.nextLong();

			if (!hm.containsKey(v[i])) {
				hm.put(v[i], 0);
			}
			hm.put(v[i], hm.get(v[i]) + 1);
		}
		Arrays.sort(v);

		long[] sum = new long[n + 1];
		for (int i = n - 1; i >= 0; i--) {
			sum[i] = sum[i + 1] + v[i];
		}

		Set<Long> hs = new HashSet<>();
		for (int i = n - 1; i >= 0; i--) {
			int c = n - i;

			if (c > b) {
				pr.printf("%.7f\n", (double)sum[n - 1]);

				long ret = 0;
				for (int j = a; j <= b; j++) {
					ret += CLong(hm.get(v[n - 1]), j);
				}

				pr.println(ret);
				break;
			} else if (c < a) {
				hs.add(v[i]);
			} else if (c == a) {
				hs.add(v[i]);

				if (hs.size() > 1) {
					pr.printf("%.7f\n", (double)sum[i] / c);

					int cnt = 0;
					for (int j = i; j < n; j++) {
						if (v[j] == v[i]) {
							cnt++;
						} else {
							break;
						}
					}

					pr.println(CLong(hm.get(v[i]), cnt));
					break;
				}
			} else {
				hs.add(v[i]);

				if (hs.size() > 1) {
					pr.printf("%.7f\n", (double)sum[i + 1] / (c - 1));

					int cnt = 0;
					for (int j = i + 1; j < n; j++) {
						if (v[j] == v[i + 1]) {
							cnt++;
						} else {
							break;
						}
					}

					pr.println(CLong(hm.get(v[i + 1]), cnt));
					break;
				}
			}
		}

		pr.printf("%.7f\n", (double)sum[n - 1]);

		long ret = 0;
		for (int j = a; j <= b; j++) {
			ret += CLong(hm.get(v[n - 1]), j);
		}

		pr.println(ret);
	}

	// 組合せの数
	// パスカルの三角形MODなし
	// 限界：n=66 : 66C33=7219428434016265740
	private final static int LIMIT = 66;
	private static int to;
	private static long[][] cache;

	private static long CLong(int n, int r) {
		if (r > n) {
			return 0;
		}

		if (n > LIMIT) {
			throw new IllegalArgumentException(Integer.toString(n));
		}

		if (cache == null) {
			cache = new long[LIMIT + 1][];
			cache[0] = new long[1];
			cache[0][0] = 1;
			to = 0;
		}

		if (cache[n] == null) {
			for (int i = to + 1; i <= n; i++) {
				cache[i] = new long[i + 1];
				for (int j = 0; j <= i; j++) {
					if (j == 0 || j == i) {
						cache[i][j] = 1;
					} else {
						if (Long.MAX_VALUE - cache[i - 1][j - 1] < cache[i - 1][j]) {
			    			throw new IllegalArgumentException("Overflow");
						} else {
							cache[i][j] = cache[i - 1][j - 1] + cache[i - 1][j];
						}
					}
				}
			}
			to = n;
		}

		return cache[n][r];
	}

	// ---------------------------------------------------
	public static void main(String[] args) {
		sc = new Scanner(System.in);
		pr = new Printer(System.out);

		solve();

		pr.close();
		sc.close();
	}

	@SuppressWarnings("unused")
	private static class Scanner {
		BufferedReader br;

		Scanner (InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}

		private boolean isPrintable(int ch) {
			return ch >= '!' && ch <= '~';
		}

		private boolean isCRLF(int ch) {
			return ch == '\n' || ch == '\r' || ch == -1;
		}

		private int nextPrintable() {
			try {
				int ch;
				while (!isPrintable(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}

				return ch;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		String next() {
			try {
				int ch = nextPrintable();
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (isPrintable(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		int nextInt() {
			try {
				// parseInt from Integer.parseInt()
				boolean negative = false;
				int res = 0;
				int limit = -Integer.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Integer.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				int multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		long nextLong() {
			try {
				// parseLong from Long.parseLong()
				boolean negative = false;
				long res = 0;
				long limit = -Long.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Long.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				long multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		float nextFloat() {
			return Float.parseFloat(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			try {
				int ch;
				while (isCRLF(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (!isCRLF(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		void close() {
			try {
				br.close();
			} catch (IOException e) {
//				throw new NoSuchElementException();
			}
		}
	}

	private static class Printer extends PrintWriter {
		Printer(PrintStream out) {
			super(out);
		}
	}
}