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#include <iostream>
#include <vector>
#include <algorithm>
#include <complex>
#include <numbers>
using namespace std;

const int FFT_THRESHOLD = 20;

void fft(vector<complex<double>>& a, bool invert) {
    int n = a.size();
    if (n == 1)
        return;

    vector<complex<double>> a0(n / 2), a1(n / 2);
    for (int i = 0; 2 * i < n; i++) {
        a0[i] = a[2*i];
        a1[i] = a[2*i+1];
    }
    fft(a0, invert);
    fft(a1, invert);

    double ang = 2 * numbers::pi_v<double> / n * (invert ? -1 : 1);
    complex<double> w(1), wn(cos(ang), sin(ang));
    for (int i = 0; 2 * i < n; i++) {
        a[i] = a0[i] + w * a1[i];
        a[i + n/2] = a0[i] - w * a1[i];
        if (invert) {
            a[i] /= 2;
            a[i + n/2] /= 2;
        }
        w *= wn;
    }
}

vector<complex<double>> mul(vector<complex<double>> x, vector<complex<double>> y) {
    int target_size = x.size() + y.size() - 1;

    if (x.size() * y.size() < FFT_THRESHOLD) {
        while (x.size() < target_size)
            x.emplace_back(0);
        for (int s = x.size() - 1; s >= 0; --s) {
            complex<double> dot(0);
            for (int i = 0; i <= s; ++i) {
                int j = s - i;
                if (j < y.size())
                    dot += x[i] * y[j];
            }
            x[s] = dot;
        }
        return x;
    }

    while ((target_size&-target_size) != target_size) {
        ++target_size;
    }
    
    while (x.size() < target_size)
        x.emplace_back(0);
    while (y.size() < target_size)
        y.emplace_back(0);

    fft(x, false);
    fft(y, false);

    for (int i = 0; i < target_size; ++i)
        x[i] *= y[i];

    fft(x, true);

    for (int i = 0; i < target_size; ++i)
        x[i].imag(0);
    return x;    
}

vector<complex<double>> prod(const vector<double> &ps, int start, int end) {
    if (start == end - 1) {
        return {ps[start], 1 - ps[start]};
    }
    int middle = (start + end) >> 1;
    return mul(prod(ps, start, middle), prod(ps, middle, end));
}

vector<double> success_prob(const vector<double>& ps, int answers, int t) {
    int allowed_fails = (answers - t) >> 1;
    vector<complex<double>> k_fails = prod(ps, 0, answers);
    vector<double> ret(k_fails.size());
    for (int i = 0; i < ret.size(); ++i)
        ret[i] = k_fails[i].real();
    return ret;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    
    int n, t;
    cin >> n >> t;

    vector<double> probs(n);
    for (int i = 0; i < n; ++i)
        cin >> probs[i];

    sort(probs.begin(), probs.end(), greater<double>());
    
    int gthalf = 0;

    for (gthalf = t % 2; gthalf < probs.size() - 1 && probs[gthalf] > 0.5; gthalf += 2);

    int start = max(t, gthalf - 2);
    vector<double> k_fails = success_prob(probs, start, t);

    int allowed_fails = (start - t) >> 1;
    double best = 0.0;
    if (allowed_fails >= 0) {
        double exam_pass = 0.0;
        for (int k = 0; k <= allowed_fails; ++k)
            exam_pass += k_fails[k];
        
        if (exam_pass > best)
            best = exam_pass;
    }

    while (k_fails.size() <= n)
        k_fails.emplace_back(0);
    for (int i = start; i < min(n, start + 2000); ++i) {
        double success = probs[i], fail = 1.0 - probs[i];
        for (int k = i+1; k > 0; --k) {
            k_fails[k] = k_fails[k] * success + k_fails[k - 1] * fail;
        }
        k_fails[0] *= success;

        int allowed_fails = ((i + 1) - t) >> 1;
        
        if (allowed_fails >= 0) {
            double exam_pass = 0.0;
            for (int k = 0; k <= allowed_fails; ++k)
                exam_pass += k_fails[k];
            
            if (exam_pass > best)
                best = exam_pass;
        }
    }

    cout.precision(8);
    cout << fixed << best << endl;
}