Problem: Esports is a form of competitive sports using video games. Dota 2 is one of the most popular competitive video games in Esports. Recently, a new video game Dota 3 was released. In Dota 3 a player can buy some relics for their hero. Relics are counters that track hero's actions and statistics in a game.

Gloria likes to play Dota 3, so she wants to buy all n available relics for her favorite hero.

Relics can be bought using an in-game currency called shards. Each relic has its own price — c_i shards for the i-th relic. A player can buy a relic using one of the following options: 

  * Pay c_i shards to buy the i-th relic; 
  * Pay x shards and randomly get one of all n relics. The probability of getting a relic is the same for all n relics. If a duplicate relic is received, then the relic is recycled and x/2 shards are given back to the player. 



Gloria wants to buy all n relics. Help her minimize the expected number of shards she spends to buy all the relics.

Input

The first line contains two integers n and x (1 ≤ n ≤ 100; 1 ≤ x ≤ 10 000) — the number of relics and the cost to receive a random relic.

The second line consists of n integers c_1, c_2, …, c_n (x ≤ c_i ≤ 10 000; ∑{c_i} ≤ 10 000) — the prices of n relics.

Output

Print a single real number — the minimum expected number of shards that Gloria must spend to buy all the relics.

The absolute or relative error should not exceed 10^{-9}.

Examples

Input


2 20
25 100


Output


47.50000000000000000


Input


4 30
60 50 60 80


Output


171.25000000000000000

Note

In the first example, the optimal strategy is to randomly get one of the two relics paying 20 shards. Then there are two scenarios. 

The first one happens if Gloria receives the first relic. Then she keeps getting random relics until she obtains the second relic. The expected number of shards to spend in this scenario is 20 + 30 = 50.

In the second scenario, Gloria initially gets the second relic. Then it is better to buy the first relic for 25 shards, so the expected number of shards to spend in this scenario is 20 + 25 = 45.

Thus, the expected number of shards to spend is (50 + 45)/(2) = 47.5.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC optimize("O3", "unroll-loops")
using namespace std;
namespace {
const int MOD107 = 1000000007;
const int MOD998 = 998244353;
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <class T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T>
using maxheap = priority_queue<T, vector<T>, less<T>>;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
struct Modular {
 private:
  long long MODVALUE = 0;
  long long val = 0;
  Modular initModular(long long val) const { return Modular(val, MODVALUE); }
  inline void validate() const {}
  inline void validate(const Modular& other) const {}

 public:
  explicit operator long long() const { return val; }
  template <class T>
  Modular& operator=(const T& other) {
    val = (other % MODVALUE + MODVALUE) % MODVALUE;
    return *this;
  }
  template <class T>
  void setMod(const T& MOD) {
    MODVALUE = MOD;
  }
  Modular& operator+=(const Modular& other) {
    validate(other);
    val += other.val;
    if (val >= MODVALUE) val -= MODVALUE;
    return *this;
  }
  Modular operator+(const Modular& other) const {
    Modular tmp = *this;
    return tmp += other;
  }
  template <class T>
  Modular& operator+=(const T& other) {
    return *this += initModular(other);
  }
  template <class T>
  Modular operator+(const T& other) const {
    return *this + initModular(other);
  }
  template <class T>
  friend Modular operator+(const T& other, const Modular& m) {
    return m.initModular(other) + m;
  }
  Modular& operator++() { return *this += 1; }
  Modular operator++(int) {
    Modular tmp = *this;
    ++*this;
    return tmp;
  }
  Modular operator-() const { return initModular(-val); }
  Modular& operator-=(const Modular& other) {
    validate(other);
    val -= other.val;
    if (val < 0) val += MODVALUE;
    return *this;
  }
  Modular operator-(const Modular& other) const {
    Modular tmp = *this;
    return tmp -= other;
  }
  template <class T>
  Modular& operator-=(const T& other) {
    return *this -= initModular(other);
  }
  template <class T>
  Modular operator-(const T& other) const {
    return *this - initModular(other);
  }
  template <class T>
  friend Modular operator-(const T& other, const Modular& m) {
    return m.initModular(other) - m;
  }
  Modular& operator--() { return *this -= 1; }
  Modular operator--(int) {
    Modular tmp = *this;
    --*this;
    return tmp;
  }
  Modular& operator*=(const Modular& other) {
    validate(other);
    val *= other.val;
    val %= MODVALUE;
    if (val < 0) val += MODVALUE;
    return *this;
  }
  Modular operator*(const Modular& other) const {
    Modular tmp = *this;
    return tmp *= other;
  }
  template <class T>
  Modular& operator*=(const T& other) {
    return *this *= initModular(other);
  }
  template <class T>
  Modular operator*(const T& other) const {
    return *this * initModular(other);
  }
  template <class T>
  friend Modular operator*(const T& other, const Modular& m) {
    return m.initModular(other) * m;
  }
  Modular pow(long long power) const {
    Modular m = *this, ans = initModular(1);
    while (power) {
      if (power & 1) ans *= m;
      m *= m;
      power >>= 1;
    }
    return ans;
  }
  Modular pow(const Modular& other) const { return pow(other.val); }
  Modular inv() const { return pow(MODVALUE - 2); }
  Modular& operator/=(const Modular& other) {
    val *= other.inv().val;
    val %= MODVALUE;
    if (val < 0) val += MODVALUE;
    return *this;
  }
  Modular operator/(const Modular& other) const {
    Modular tmp = *this;
    return tmp /= other;
  }
  template <class T>
  Modular& operator/=(const T& other) {
    return *this /= initModular(other);
  }
  template <class T>
  Modular operator/(const T& other) const {
    return *this / initModular(other);
  }
  template <class T>
  friend Modular operator/(const T& other, const Modular& m) {
    return m.initModular(other) / m;
  }
  friend istream& operator>>(istream& in, Modular& m) {
    in >> m.val;
    m.val %= m.MODVALUE;
    if (m.val < 0) m.val += m.MODVALUE;
    return in;
  }
  friend ostream& operator<<(ostream& out, const Modular& m) {
    return out << m.val;
  }
  Modular() {
    val = 0;
    MODVALUE = 0;
  }
  Modular(long long val, long long MOD)
      : MODVALUE(MOD), val((val % MOD + MOD) % MOD) {}
};
using Mint = Modular;
inline ll binpow(ll b, ll p, ll mod) {
  b %= mod;
  ll ans = 1;
  for (; p > 0; p >>= 1) {
    if (p & 1) {
      ans *= b;
      ans %= mod;
    }
    b *= b;
    b %= mod;
  }
  return ans;
}
inline ll max(ll a, int b) { return (a > b ? a : b); }
inline ll max(int a, ll b) { return (a > b ? a : b); }
inline ll min(ll a, int b) { return (a < b ? a : b); }
inline ll min(int a, ll b) { return (a < b ? a : b); }
template <class T>
inline bool chkmin(T& x, const T& y) {
  return x > y ? x = y, 1 : 0;
}
template <class T>
inline bool chkmax(T& x, const T& y) {
  return x < y ? x = y, 1 : 0;
}
}  // namespace
namespace IO {
template <class T>
inline void _R(T& x) {
  cin >> x;
}
template <class T1, class T2>
inline void _R(pair<T1, T2>& x) {
  _R(x.first);
  _R(x.second);
}
template <class T>
inline void _R(vector<T>& x) {
  for (auto& i : x) _R(i);
}
template <class T>
inline void _R(deque<T>& x) {
  for (auto& i : x) _R(i);
}
inline void R() {}
template <class T1, class... T2>
inline void R(T1& x, T2&... y) {
  _R(x);
  R(y...);
}
template <class T>
inline void _W(const T& x);
template <class T1, class T2>
inline void _W(const pair<T1, T2>& p);
template <class... T>
inline void _W(const vector<T...>& x);
template <class... T>
inline void _W(const deque<T...>& x);
template <class... T>
inline void _W(const forward_list<T...>& x);
template <class... T>
inline void _W(const list<T...>& x);
template <class... T>
inline void _W(const set<T...>& x);
template <class... T>
inline void _W(const multiset<T...>& x);
template <class... T>
inline void _W(const unordered_set<T...>& x);
template <class... T>
inline void _W(const unordered_multiset<T...>& x);
template <class... T>
inline void _W(const map<T...>& x);
template <class... T>
inline void _W(const multimap<T...>& x);
template <class... T>
inline void _W(const unordered_map<T...>& x);
template <class... T>
inline void _W(const unordered_multimap<T...>& x);
template <class Container>
inline void printContainer(const Container& x) {
  bool isFirst = 1;
  for (auto i : x) {
    if (!isFirst) cout << ' ';
    isFirst = 0;
    _W(i);
  }
}
template <class T>
inline void _W(const T& x) {
  cout << x;
}
template <class T1, class T2>
inline void _W(const pair<T1, T2>& p) {
  _W(p.first);
  _W(' ');
  _W(p.second);
}
template <class... T>
inline void _W(const vector<T...>& x) {
  printContainer(x);
}
template <class... T>
inline void _W(const deque<T...>& x) {
  printContainer(x);
}
template <class... T>
inline void _W(const forward_list<T...>& x) {
  printContainer(x);
}
template <class... T>
inline void _W(const list<T...>& x) {
  printContainer(x);
}
template <class... T>
inline void _W(const set<T...>& x) {
  printContainer(x);
}
template <class... T>
inline void _W(const multiset<T...>& x) {
  printContainer(x);
}
template <class... T>
inline void _W(const unordered_set<T...>& x) {
  printContainer(x);
}
template <class... T>
inline void _W(const unordered_multiset<T...>& x) {
  printContainer(x);
}
template <class... T>
inline void _W(const map<T...>& x) {
  printContainer(x);
}
template <class... T>
inline void _W(const multimap<T...>& x) {
  printContainer(x);
}
template <class... T>
inline void _W(const unordered_map<T...>& x) {
  printContainer(x);
}
template <class... T>
inline void _W(const unordered_multimap<T...>& x) {
  printContainer(x);
}
inline void W() { cout << '\n'; }
template <class T>
inline void W(const T& x) {
  _W(x);
  W();
}
template <class T1, class... T2>
inline void W(const T1& x, const T2&... y) {
  _W(x);
  _W(' ');
  W(y...);
}
}  // namespace IO
using namespace IO;
namespace outputFormat {
inline string Case(int tc) { return "Case #" + to_string(tc) + ':'; }
inline string YN(bool b) { return b ? "Yes" : "No"; }
}  // namespace outputFormat
using namespace outputFormat;
namespace std {
template <class T1, class T2>
struct hash<pair<T1, T2>> {
  std::size_t operator()(pair<T1, T2> _) const {
    return hash<T1>{}(_.first) ^ hash<T2>{}(_.second);
  }
};
}  // namespace std
int main() {
  ll n, x;
  R(n, x);
  vector<ll> a(n);
  R(a);
  const ll sum = accumulate((a).begin(), (a).end(), 0);
  vector<vector<double>> ways(n + 1, vector<double>(sum + 1, 0));
  ways[0][0] = 1;
  for (auto& i : a)
    for (int sz = n - 1; sz >= 0; sz--)
      for (int val = 0; val + i <= sum; val++)
        ways[sz + 1][val + i] += ways[sz][val];
  vector<double> plog(n + 1, 0);
  for (int i = 2; i <= n; i++) plog[i] = plog[i - 1] + log2(i);
  double ans = 0;
  for (int sz = 0; sz < n; sz++) {
    for (int val = 0; val <= sum; val++) {
      double buy = 1.0 * (sum - val) / (n - sz);
      double random = (1.0 * n / (n - sz) + 1) * x / 2;
      ans += 1.0 * ways[sz][val] * pow(2, plog[sz] + plog[n - sz] - plog[n]) *
             min(buy, random);
    }
  }
  W(ans);
  return 0;
}
static auto __init__ = []() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(10);
  return 42;
}();