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#include <bits/stdc++.h>
using namespace std;

#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define all(x) begin(x), end(x)
#define sz(x) int((x).size())
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;

#ifdef LOCAL
auto operator<<(auto& o, auto x) -> decltype(x.first, o);
auto operator<<(auto& o, auto x) -> decltype(x.end(), o) {
  o << "{";
  for (int i = 0; auto y : x) o << ", " + !i++ * 2 << y;
  return o << "}"; }
auto operator<<(auto& o, auto x) -> decltype(x.first, o) {
  return o << "(" << x.first << ", " << x.second << ")"; }
void __print(auto... x) { ((cerr << x << " "), ...) << endl; }
#define debug(x...) __print("[" #x "]:", x)
#else
#define debug(...) 2137
#endif

const double eps = 1e-12;
const int nax = 1e5 + 10;
vector<double> poly[nax];
double dp[nax], ndp[nax];

typedef complex<double> C;
typedef vector<double> vd;
void fft(vector<C>& a) {
  int n = sz(a), L = 31 - __builtin_clz(n);
  static vector<complex<long double>> R(2, 1);
  static vector<C> rt(2, 1);  // (^ 10% faster if double)
  for (static int k = 2; k < n; k *= 2) {
    R.resize(n); rt.resize(n);
    auto x = polar(1.0L, acos(-1.0L) / k);
    rep(i,k,2*k) rt[i] = R[i] = i&1 ? R[i/2] * x : R[i/2];
  }
  vi rev(n);
  rep(i,0,n) rev[i] = (rev[i / 2] | (i & 1) << L) / 2;
  rep(i,0,n) if (i < rev[i]) swap(a[i], a[rev[i]]);
  for (int k = 1; k < n; k *= 2)
    for (int i = 0; i < n; i += 2 * k) rep(j,0,k) {
      // C z = rt[j+k] * a[i+j+k]; // (25% faster if hand-rolled)  /// include-line
      auto x = (double *)&rt[j+k], y = (double *)&a[i+j+k];        /// exclude-line
      C z(x[0]*y[0] - x[1]*y[1], x[0]*y[1] + x[1]*y[0]);           /// exclude-line
      a[i + j + k] = a[i + j] - z;
      a[i + j] += z;
    }
}
vd conv(const vd& a, const vd& b) {
  if (a.empty() || b.empty()) return {};
  vd res(sz(a) + sz(b) - 1);
  int L = 32 - __builtin_clz(sz(res)), n = 1 << L;
  vector<C> in(n), out(n);
  copy(all(a), begin(in));
  rep(i,0,sz(b)) in[i].imag(b[i]);
  fft(in);
  for (C& x : in) x *= x;
  rep(i,0,n) out[i] = in[-i & (n - 1)] - conj(in[i]);
  fft(out);
  rep(i,0,sz(res)) res[i] = imag(out[i]) / (4 * n);
  return res;
}

vd rec(int l, int r) {
  if(l + 1 == r) return poly[l];
  int m = (l + r) >> 1;
  auto a = rec(l, m);
  auto b = rec(m, r);
  auto c = conv(a, b);
  return c;
}

double get(int n, int t)  {
  int ind = (n + t) / 2;
  auto res = rec(0, n + 1);
  double sum = 0;
  for(int i = 0; i <= ind && i < res.size(); i++) {
    sum += res[i];
  }
  return 1 - sum;
}

double phi(double x) {
  return erfc(-x / sqrt(2)) / 2.0;
}

int main() {
  cin.tie(0)->sync_with_stdio(0);
  cout << fixed << setprecision(9);

  int n, t;
  cin >> n >> t;
  vector<double> p(n);
  for(int i = 0; i < n; i++) {
    cin >> p[i];
  }
  sort(p.rbegin(), p.rend());

  while(p.size() && p.back() < eps) p.pop_back();
  reverse(all(p));
  while(p.size() && p.back() > 1 - eps) {
    p.pop_back();
    t--;
  }
  if(t <= 0) {
    cout << 1.0 << endl;
    return 0;
  }
  reverse(all(p));
  n = p.size();

  for(int i = 0; i <= 2 * n; i++) {
    dp[i] = ndp[i] = 1;
  }
  double res = 0, mu = 0, var = 0;
  const int bnd = 2000;
  for(int i = 0; i < min(n, bnd); i++) {
    mu += p[i];
    var += p[i] * (1 - p[i]);
    ndp[0] = dp[0] * (1 - p[i]);
    for(int j = 1; j <= i + 1; j++) {
      ndp[j] = dp[j - 1] * p[i] + dp[j] * (1 - p[i]);
    }
    swap(dp, ndp);
    res = max(res, 1 - dp[(i + t) / 2]);
  }

  vector<pair<double, int>> cand;
  for(int i = bnd; i < n; i++) {
    mu += p[i];
    var += p[i] * (1 - p[i]);
    double arg = (i + t) / 2.0;
    double x = 1 - phi((arg - mu) / sqrt(var));
    cand.push_back({x, i});
  }
  sort(cand.rbegin(), cand.rend());

  for(int i = 0; i < n; i++) {
    poly[i] = {1 - p[i], p[i]};
  }
  for(int i = 0; i < min(12, sz(cand)); i++) {
    int ind = cand[i].second;
    double x = get(ind, t);
    res = max(res, x);
  }
  cout << res << endl;
}