Problem: Kleofáš is participating in an n-thlon - a tournament consisting of n different competitions in n different disciplines (numbered 1 through n). There are m participants in the n-thlon and each of them participates in all competitions.

In each of these n competitions, the participants are given ranks from 1 to m in such a way that no two participants are given the same rank - in other words, the ranks in each competition form a permutation of numbers from 1 to m. The score of a participant in a competition is equal to his/her rank in it.

The overall score of each participant is computed as the sum of that participant's scores in all competitions.

The overall rank of each participant is equal to 1 + k, where k is the number of participants with strictly smaller overall score.

The n-thlon is over now, but the results haven't been published yet. Kleofáš still remembers his ranks in each particular competition; however, he doesn't remember anything about how well the other participants did. Therefore, Kleofáš would like to know his expected overall rank.

All competitors are equally good at each discipline, so all rankings (permutations of ranks of everyone except Kleofáš) in each competition are equiprobable.

Input

The first line of the input contains two space-separated integers n (1 ≤ n ≤ 100) and m (1 ≤ m ≤ 1000) — the number of competitions and the number of participants respectively.

Then, n lines follow. The i-th of them contains one integer xi (1 ≤ xi ≤ m) — the rank of Kleofáš in the i-th competition.

Output

Output a single real number – the expected overall rank of Kleofáš. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 9.

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.

Examples

Input

4 10
2
1
2
1


Output

1.0000000000000000


Input

5 5
1
2
3
4
5


Output

2.7500000000000000


Input

3 6
2
4
2


Output

1.6799999999999999

Note

In the first sample, Kleofáš has overall score 6. Nobody else can have overall score less than 6 (but it's possible for one other person to have overall score 6 as well), so his overall rank must be 1.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline T checkbit(T n, T i) {
  T n_ = n;
  return ((n_ >> i) & T(1));
}
template <typename T>
inline T bitcount(T n) {
  T n_ = n;
  return __builtin_popcount(n_);
}
template <typename T>
inline T isPowerOfTwo(T n) {
  T n_ = n;
  return (n_ != 0 and ((n_ & (n_ - 1)) == 0));
}
template <typename T>
inline T sqr(T x) {
  T x_ = (x);
  return x_ * x_;
}
template <typename T>
inline T qbr(T x) {
  T x_ = (x);
  return ((x_ * x_) * x_);
}
template <typename T>
inline T mod(T x, T m) {
  T x_ = (x);
  return (((x_) >= 0) ? ((x_) % (m)) : ((((x_) % (m)) + (m)) % (m)));
}
template <typename T>
inline T gcd(T a, T b) {
  while (b) {
    T t = a % b;
    a = b;
    b = t;
  }
  return a;
}
template <typename T>
inline T gcd_ex(T a, T b, T& x, T& y) {
  if (b == 0) {
    x = 1, y = 0;
    return a;
  }
  T x1, y1;
  T d = gcd_ex(b, a % b, x1, y1);
  x = y1;
  y = x1 - (a / b) * y1;
  return d;
}
template <typename T>
inline T lcm(T a, T b) {
  return (a * (b / gcd(a, b)));
}
template <typename Collection, typename UnaryOperation>
void foreach (Collection& col, UnaryOperation op) {
  for_each(begin(col), end(col), op);
}
template <typename Collection, typename UnaryOperation>
Collection fmap(Collection& col, UnaryOperation op) {
  transform(begin(col), end(col), col.begin(), op);
  return col;
}
template <typename Collection, typename binop>
Collection zip(Collection& fc, Collection& sc, binop op) {
  transform(begin(fc), end(fc), sc.begin(), fc.begin(), op);
  return fc;
}
template <typename Collection, typename Condition>
bool exists(Collection& col, Condition con) {
  auto exist = find_if(begin(col), end(col), con);
  return exist != col.end();
}
template <typename Collection, typename Predicate>
Collection filterNot(Collection& col, Predicate predicate) {
  auto returnIterator = remove_if(begin(col), end(col), predicate);
  col.erase(returnIterator, end(col));
  return col;
}
template <class T1, class T2>
istream& operator>>(istream& in, pair<T1, T2>& P) {
  in >> P.first >> P.second;
  return in;
}
template <class T>
istream& operator>>(istream& in, vector<T>& Col) {
  for (auto& el : Col) in >> el;
  return in;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const vector<vector<T>>& v) {
  for (auto& row : v) {
    for (auto& el : row) os << el << " ";
    os << "\n";
  }
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& Col) {
  for (auto& el : Col) os << el << " ";
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& Col) {
  for (auto& el : Col) os << el << " ";
  return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& Col) {
  for (auto& el : Col) os << el << " ";
  return os;
}
template <typename First>
void read(First& t) {
  cin >> t;
}
template <typename First, typename... Args>
void read(First& f, Args&... args) {
  cin >> f;
  read(forward<Args&>(args)...);
}
template <typename T>
void print(T&& t) {
  cout << t << "\n";
}
template <typename First, typename... Args>
void print(First&& f, Args&&... args) {
  cout << f << " ";
  print(forward<Args&&>(args)...);
}
template <typename T>
void printLn(T&& t) {
  cout << t << "\n";
}
template <typename First, typename... Args>
void printLn(First&& f, Args&&... args) {
  cout << f << "\n";
  printLn(forward<Args&&>(args)...);
}
template <typename T, size_t N>
struct MakeTensor {
  template <typename... Args>
  static auto make_tensor(size_t first, Args... sizes)
      -> vector<decltype(MakeTensor<T, N - 1>::make_tensor(sizes...))> {
    auto inner = MakeTensor<T, N - 1>::make_tensor(sizes...);
    return vector<decltype(inner)>(first, inner);
  }
};
template <typename T>
struct MakeTensor<T, 1> {
  static vector<T> make_tensor(size_t size) { return vector<T>(size); }
};
template <typename T, typename... Args>
auto make_tensor(Args... args)
    -> decltype(MakeTensor<T, sizeof...(Args)>::make_tensor(args...)) {
  return MakeTensor<T, sizeof...(Args)>::make_tensor(args...);
}
const int MAXCOMP = 100, MAXPTS = 100 * 1000;
double P[MAXCOMP + 10][2 * MAXPTS + 1];
int pos[MAXCOMP + 10];
int main() {
  int n, m;
  read(n, m);
  P[0][0] = 1.0;
  P[0][1] = -1.0;
  int my_points = 0;
  for (int i = 1; i <= n; i++) {
    read(pos[i]);
    my_points += pos[i];
  }
  if (m == 1) {
    print("1.00000000000\n");
    exit(0);
  }
  for (int i = 0; i <= n; i++) {
    int banned_points = pos[i + 1];
    for (int points = 1; points <= my_points; points++) {
      P[i][points] += P[i][points - 1];
    }
    for (int points = 0; points <= my_points; points++) {
      if (P[i][points] > (double)1e-16) {
        double probability = P[i][points] / double(m - 1);
        P[i + 1][points + 1] += probability;
        P[i + 1][points + banned_points] -= probability;
        P[i + 1][points + banned_points + 1] += probability;
        P[i + 1][points + m + 1] -= probability;
      }
    }
  }
  double answer = 0;
  for (int i = 1; i < my_points; i++) {
    answer += P[n][i];
  }
  answer = answer * (m - 1) + 1.0;
  cout << fixed << setprecision(15) << answer << "\n";
}