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// clang-format off
#include<bits/stdc++.h>
using namespace std;
using LL=long long;
#define FOR(i,l,r) for(auto i=(l);i<=(r);++i)
#define REP(i,n) FOR(i,0,(n)-1)
#define ssize(x) int(x.size())
template<class A,class B>auto&operator<<(ostream&o,pair<A,B>p){return o<<"("<<p.first<<", "<<p.second<<")";}
template<class T>auto operator<<(ostream&o,T x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<(", ")+2*!i++<<e;return o<<"}";}
#ifdef DEBUG
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<"\n";}(X)
#else
#define debug(...) {}
#endif
// clang-format on

using r_t               = double;
const int avg_window    = 2;
const int query_base    = 2048;
const int search_window = query_base * 2;
const int out_precision = 7;
const int min_fft_exp   = 11;
const int max_fft_exp   = 17;
const int ncache_exps   = max_fft_exp - 1;
const int ops_thres     = 700 * 700;

struct FFT
{
    int n;
    vector<int> perm;
    using cd = complex<double>;
    FFT(int n);
    void fft(vector<cd>& a, bool invert) const;
};
FFT ffts[max_fft_exp + 1] = {
  FFT(1 << 0),
  FFT(1 << 1),
  FFT(1 << 2),
  FFT(1 << 3),
  FFT(1 << 4),
  FFT(1 << 5),
  FFT(1 << 6),
  FFT(1 << 7),
  FFT(1 << 8),
  FFT(1 << 9),
  FFT(1 << 10),
  FFT(1 << 11),
  FFT(1 << 12),
  FFT(1 << 13),
  FFT(1 << 14),
  FFT(1 << 15),
  FFT(1 << 16),
  FFT(1 << 17),
};

int N, thres;
vector<array<pair<bool, vector<r_t>>, ncache_exps>> PMF_cache;
vector<r_t> buffer;

// PMF calculation
void brute_conv(const vector<r_t>& A, const vector<r_t>& B, vector<r_t>& out);
void get_conv(const vector<r_t>& A, const vector<r_t>& B, vector<r_t>& out);
const vector<r_t>& get_PMF_cache(int k, int exp);
vector<r_t> starter_PMF(int k);
void advance_PMF(int k, const vector<r_t>& PMF, vector<r_t>& out);

// Getting score
int thres_to_succ(int k);
r_t PMF_to_score(const vector<r_t>& PMF, int k);
r_t get_func(int k);
int get_search_start(int L, int R);

int
main()
{
    cin.tie(0)->sync_with_stdio(0);
    cerr << fixed << setprecision(30);
    cout << fixed << setprecision(out_precision);
    cin >> N >> thres;
    {
        vector<r_t> ps(N);
        for (auto& p : ps) cin >> p;
        sort(ps.begin(), ps.end(), greater<r_t>());

        // Create PMF cache
        PMF_cache.resize(N);
        REP (i, N) PMF_cache[i][0] = {true, {1 - ps[i], ps[i]}};
    }

    // Range in which we will search for a good starting point
    int L = thres - thres % query_base, R = N - avg_window + 1;
    int search_start = get_search_start(L, R);
    debug(L, R, search_start);

    // Search brutally through the search window
    auto PMF        = starter_PMF(search_start);
    auto best_score = max<r_t>(0, PMF_to_score(PMF, search_start));
    L = search_start + 1, R = min(N, search_start + search_window - 1);
    FOR (k, L, R) {
        advance_PMF(k, PMF, buffer);
        swap(PMF, buffer);
        auto score = PMF_to_score(PMF, k);
        best_score = max(best_score, score);
    }
    cout << best_score << "\n";
    return 0;
}

int
get_search_start(int L, int R)
{
    r_t max_val = 0;
    int max_pos = 0;
    for (int k = L; k <= R; k += query_base) {
        auto val = get_func(k);
        if (val > max_val) max_val = val, max_pos = k;
    }
    return max(L, max_pos - query_base);
}

int
thres_to_succ(int k)
{
    return (thres + k + 1) / 2;
}

r_t
PMF_to_score(const vector<r_t>& PMF, int k)
{
    k       = thres_to_succ(k);
    r_t res = 0;
    FOR (i, k, ssize(PMF) - 1) res += PMF[i];
    return res;
}

r_t
get_func(int k)
{
    auto PMF = starter_PMF(k);
    advance_PMF(k + 1, PMF, buffer);
    auto res = PMF_to_score(PMF, k) + PMF_to_score(buffer, k + 1);
    return res;
}

vector<r_t>
starter_PMF(int k)
{
    vector<r_t> out = {1};
    int i = 0, exp = ncache_exps - 1, span = 1 << exp;
    while (k) {
        while (span > k) --exp, span >>= 1;
        get_conv(get_PMF_cache(i, exp), out, buffer);
        swap(buffer, out);
        i += span, k -= span;
    }
    return out;
}

void
advance_PMF(int k, const vector<r_t>& PMF, vector<r_t>& out)
{
    const auto& p = PMF_cache[k - 1][0].second;
    out.resize(ssize(PMF) + 1);
    out[0] = PMF[0] * p[0], out.back() = PMF.back() * p[1];
    FOR (i, 1, ssize(PMF) - 1) out[i] = PMF[i - 1] * p[1] + PMF[i] * p[0];
}

const vector<r_t>&
get_PMF_cache(int k, int exp)
{
    auto& entry = PMF_cache[k][exp];
    if (!entry.first) {
        entry.first = true;
        get_conv(get_PMF_cache(k, exp - 1),
                 get_PMF_cache(k + (1 << (exp - 1)), exp - 1),
                 entry.second);
    }
    return entry.second;
}

void
brute_conv(const vector<r_t>& A, const vector<r_t>& B, vector<r_t>& out)
{
    out.assign(ssize(A) + ssize(B) - 1, 0);
    REP (b, ssize(B))
        REP (a, ssize(A)) out[a + b] += A[a] * B[b];
}

void
get_conv(const vector<r_t>& A, const vector<r_t>& B, vector<r_t>& out)
{
    // Maybe brut is fast enough
    if (ssize(A) * ssize(B) < ops_thres) {
        brute_conv(A, B, out);
        return;
    }

    // Select appropriate FFT for the task
    int final_size = ssize(A) + ssize(B) - 1, exp = 0, buf_size = 1;
    while (buf_size < final_size) ++exp, buf_size <<= 1;
    if (exp < min_fft_exp) {
        brute_conv(A, B, out);
        return;
    }
    const auto& fft = ffts[exp];

    // Calculate DFT for A
    vector<FFT::cd> Ai(buf_size);
    REP (i, ssize(A)) Ai[fft.perm[i]] = A[i];
    fft.fft(Ai, false);

    // Calculate DFT for B
    vector<FFT::cd> Bi(buf_size);
    REP (i, ssize(B)) Bi[fft.perm[i]] = B[i];
    fft.fft(Bi, false);

    // Get convolution
    REP (i, buf_size) Bi[i] *= Ai[i];
    REP (i, buf_size) Ai[fft.perm[i]] = Bi[i];
    fft.fft(Ai, true);

    // Prepare output
    out.resize(final_size);
    REP (i, final_size) out[i] = max<r_t>(0, Ai[i].real());
}

FFT::FFT(int n)
  : n(n)
  , perm(n)
{
    iota(perm.begin(), perm.end(), 0);
    for (int i = 1, j = 0; i < n; i++) {
        int bit = n >> 1;
        for (; j & bit; bit >>= 1) j ^= bit;
        j ^= bit;
        if (i < j) swap(perm[i], perm[j]);
    }
};

void
FFT::fft(vector<cd>& a, bool invert) const
{
    for (int len = 2; len <= n; len <<= 1) {
        double ang = 2 * std::numbers::pi / len * (invert ? -1 : 1);
        cd wlen(cos(ang), sin(ang));
        for (int i = 0; i < n; i += len) {
            cd w(1);
            for (int j = 0; j < len / 2; j++) {
                cd u = a[i + j], v = a[i + j + len / 2] * w;
                a[i + j]           = u + v;
                a[i + j + len / 2] = u - v;
                w *= wlen;
            }
        }
    }

    if (invert) {
        for (cd& x : a) x /= n;
    }
}