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 CPP):

Solution:
#if 0
date +%Y.%m.%d

  先放长度最大的弧，然后根据其位置把环转成链，问题变为连续的线段覆盖问题。
  注意到长度都是整数，那么只要枚举剩下所有弧的位置的小数部分的大小关系，问题就可以转换
为离散的线段覆盖，而所有弧的小数部分是独立同分布随机变量，因此每种大小关系是等概率出现
的。
  既然小数部分的大小关系已经确定，不妨设其为 1/n, 2/n, ... ，那么问题就是在长为 C * n
的链上做离散的线段覆盖问题，DP 设 f[S][i] 表示用 S 集合内的线段，恰好覆盖 [0, i] 的方
案数。不重不漏的转移需要枚举左端点最右边的线段，实现可以直接从小到大枚举左端点，再枚举
状态进行插入线段的转移。
#endif
#include <cstdio>
#include <cstring>
#include <algorithm>
#define debug(...) fprintf(stderr, __VA_ARGS__)

typedef long long ll;
typedef long double ld;

struct {
	inline operator int () { int x; return scanf("%d", &x), x; }
	template<class T> inline void operator () (T &x) { x = *this; }
} read;

const int maxn = 6, maxc = 50;
int len[maxn], p[maxn];
ll f[1 << maxn][maxc * maxn + 1];

int main () {
	int n = read, c = read;
	for (int i = 0; i < n; i ++) read(len[i]);
	std::sort(len, len + n);

	ll ans = 0, tot = 0;
	for (int i = 1; i < n; i ++) p[i] = i - 1;
	do {
		int U = (1 << n >> 1) - 1;
		memset(f, 0, sizeof f);
		int min = len[n - 1] * n;
		f[0][min] = 1;
		for (int l = 0, i; l < c * n; l ++)
			if ((i = l % n)) {
				i = p[i];
				int r = std::min(c * n, l + len[i] * n);
				for (int S = 0; S <= U; S ++)
					if (!(S >> i & 1))
						for (int k = l; k <= c * n; k ++)
							f[S | (1 << i)][std::max(k, r)] += f[S][k];
			}
		ans += f[U][c * n];
		++ tot;
	} while (std::next_permutation(p + 1, p + n));

	ld Ans = ans;
	Ans /= tot;
	for (int i = 0; i < n - 1; i ++)
		Ans /= c;
	printf("%.12Lf\n", Ans);
}