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#include <bits/stdc++.h>
using namespace std;
#define fwd(i, a, n) for (int i = (a); i < (n); i++)
#define rep(i, n)    fwd(i, 0, n)
#define all(X)       X.begin(), X.end()
#define sz(X)        int(size(X))
#define pb           push_back
#define eb           emplace_back
#define st           first
#define nd           second
using pii = pair<int, int>;
using vi = vector<int>;
using ll = long long;
using ld = long double;
#ifdef LOC
auto SS = signal(6, [](int) {
	*(int *)0 = 0;
});
#	define DTP(x, y)                                      \
		auto operator<<(auto &o, auto a)->decltype(y, o) { \
			o << "(";                                      \
			x;                                             \
			return o << ")";                               \
		}
DTP(o << a.st << ", " << a.nd, a.nd);
DTP(for (auto i : a) o << i << ", ", all(a));
void dump(auto... x) {
	((cerr << x << ", "), ...) << '\n';
}
#	define deb(x...) cerr << setw(4) << __LINE__ << ":[" #x "]: ", dump(x)
#else
#	define deb(...) 0
#endif

// Z liba:
// https://github.com/KacperTopolski/kactl/blob/main/content/numerical/FastFourierTransform.h

typedef complex<ld> C;
typedef vector<ld> 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);
		fwd(i, k, 2 * k) rt[i] = R[i] = i & 1 ? R[i / 2] * x : R[i / 2];
	}
	vi rev(n);
	rep(i, n) rev[i] = (rev[i / 2] | (i & 1) << L) / 2;
	rep(i, 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, k) {
				// C z = rt[j+k] * a[i+j+k]; // (25% faster if hand-rolled)  ///
				// include-line
				auto x = (ld *)&rt[j + k],
					 y = (ld *)&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, sz(b)) in[i].imag(b[i]);
	fft(in);
	for (C &x : in)
		x *= x;
	rep(i, n) out[i] = in[-i & (n - 1)] - conj(in[i]);
	fft(out);
	rep(i, sz(res)) res[i] = imag(out[i]) / (4 * n);
	return res;
}

constexpr int block_size = 1500;

void sol() {
	int n, t;
	cin >> n >> t;
	vd p(n);
	rep(i, n) cin >> p[i];
	sort(all(p), greater<ld>());
	int start = t % 2;
	while ((n - start) % (2 * block_size) != 0) {
		n += 1;
		p.pb(0);
	}
	ld max_prob = 0, tot_prob = 0;
	vd dp;
	if (start == 1) {
		dp = {1 - p[0], p[0]};
		if (t == 1)
			max_prob = tot_prob = dp[1];
	} else {
		dp = {1};
	}
	vd naive_dp(2 * block_size + 1);
	for (int block_l = start; block_l < n; block_l += 2 * block_size) {
		fill(all(naive_dp), 0);
		naive_dp[0] = 1;
		ld new_tot_prob = tot_prob;
		for (int i = 0; i < 2 * block_size; i += 2) {
			ld prob_first = p[block_l + i], prob_second = p[block_l + i + 1];
			ld prob_c_first = 1 - prob_first, prob_c_second = 1 - prob_second;
			ld prob_none = prob_c_first * prob_c_second;
			ld prob_one =
				prob_first * prob_c_second + prob_c_first * prob_second;
			ld prob_two = prob_first * prob_second;
			for (int j = i + 2; j >= 2; j--)
				naive_dp[j] = naive_dp[j] * prob_none +
							  naive_dp[j - 1] * prob_one +
							  naive_dp[j - 2] * prob_two;
			naive_dp[1] = naive_dp[1] * prob_none + naive_dp[0] * prob_one;
			naive_dp[0] *= prob_none;
			int dp_threshold = (t + block_l) / 2;
			int threshold_delta = i / 2 + 1;
			new_tot_prob = tot_prob;
			int a = dp_threshold - threshold_delta;
			int b = dp_threshold;
			ld jump_sum = 0;
			rep(j, threshold_delta) {
				jump_sum += naive_dp[2 * threshold_delta - j];
				if (a + j >= 0 && a + j < sz(dp))
					new_tot_prob += dp[a + j] * jump_sum;
			}
			rep(j, threshold_delta) {
				jump_sum += naive_dp[threshold_delta - j];
				if (b + j >= 0 && b + j < sz(dp))
					new_tot_prob += dp[b + j] * (jump_sum - 1);
			}
			max_prob = max(max_prob, new_tot_prob);
		}
		dp = conv(dp, naive_dp);
		tot_prob = new_tot_prob;
	}
	cout << max_prob << '\n';
}

int32_t main() {
	cin.tie(0)->sync_with_stdio(0);
	cout << fixed << setprecision(15);
	sol();
#ifdef LOCF
	cout.flush();
	cerr << "- - - - - - - - -\n";
	(void)!system(
		"grep VmPeak /proc/$PPID/status | sed s/....kB/\' MB\'/1 >&2"); // 4x.kB
																		// ....kB
#endif
}