Problem: You have a circle of length C, and you are placing N arcs on it. Arc i has length L_i.

Every arc i is placed on the circle uniformly at random: a random real point on the circle is chosen, then an arc of length L_i centered at this point appears.

Note that the arcs are placed independently. For example, they may intersect or contain each other.

What is the probability that every real point of the circle will be covered by at least one arc? Assume that an arc covers its ends.

Constraints

* 2 \leq N \leq 6
* 2 \leq C \leq 50
* 1 \leq L_i < C
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N C
L_1 L_2 ... L_N


Output

Print the probability that every real point of the circle will be covered by at least one arc. Your answer will be considered correct if its absolute error doesn't exceed 10^{-11}.

Examples

Input

2 3
2 2


Output

0.3333333333333333


Input

4 10
1 2 3 4


Output

0.0000000000000000


Input

4 2
1 1 1 1


Output

0.5000000000000000


Input

3 5
2 2 4


Output

0.4000000000000000


Input

4 6
4 1 3 2


Output

0.3148148148148148


Input

6 49
22 13 27 8 2 19


Output

0.2832340720702695

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {

	int solve(int[] a, int[] p, int c) {
		int n = a.length;
		int[][] dp = new int[1 << (n - 1)][c * n + 1];
		dp[0][n * a[n - 1]] = 1;

		for (int i = 0; i < c * n; i++) {
			
//			System.err.println(Arrays.deepToString(dp));

			for (int mask = (1 << (n - 1)) - 1; mask >= 0; mask--) {
				for (int ok = i; ok <= c * n; ok++) {
					if (dp[mask][ok] == 0) {
						continue;
					}

					if (i % n != 0) {
						int who = p[i % n - 1];
						if (!test(mask, who)) {
							dp[mask | (1 << who)][Math.min(
									Math.max(ok, i + n * a[who]), c * n)] += dp[mask][ok];
						}
					}

				}
			}
		}

		return dp[(1 << (n - 1)) - 1][c * n];
	}

	static boolean test(int mask, int i) {
		return ((mask >> i) & 1) == 1;
	}

	void submit() {
		int n = nextInt();
		int c = nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
		}
		Arrays.sort(a);

		int[] p = new int[n - 1];
		for (int i = 0; i < p.length; i++) {
			p[i] = i;
		}

		long good = 0;
		long total = 0;
		long one = BigInteger.valueOf(c).pow(n - 1).intValueExact();

		do {
			good += solve(a, p, c);
			total += one;
		} while (nextPermutation(p));

		out.println(1.0 * good / total);
	}

	static boolean nextPermutation(int[] a) {
		int n = a.length;
		int ptr = n - 1;
		while (ptr > 0 && a[ptr - 1] >= a[ptr]) {
			ptr--;
		}

		for (int i = ptr, j = n - 1; i < j; i++, j--) {
			int tmp = a[i];
			a[i] = a[j];
			a[j] = tmp;
		}

		if (ptr == 0) {
			return false;
		}

		for (int i = ptr;; i++) {
			if (a[ptr - 1] < a[i]) {
				int tmp = a[ptr - 1];
				a[ptr - 1] = a[i];
				a[i] = tmp;
				return true;
			}
		}
	}

	void preCalc() {

	}

	void stress() {

	}

	void test() {

	}

	Main() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		preCalc();
		submit();
		// stress();
		// test();
		out.close();
	}

	static final Random rng = new Random();

	static int rand(int l, int r) {
		return l + rng.nextInt(r - l + 1);
	}

	public static void main(String[] args) throws IOException {
		new Main();
	}

	BufferedReader br;
	PrintWriter out;
	StringTokenizer st;

	String nextToken() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return st.nextToken();
	}

	String nextString() {
		try {
			return br.readLine();
		} catch (IOException e) {
			throw new RuntimeException(e);
		}
	}

	int nextInt() {
		return Integer.parseInt(nextToken());
	}

	long nextLong() {
		return Long.parseLong(nextToken());
	}

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