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// Author: Olaf Surgut (surgutti)
// Created on 11-03-2025 12:27:37
#include "bits/stdc++.h"
using namespace std;

#define int long long
#define ll long long
#define ld long double

#define endl '\n'
#define st first
#define nd second
#define pb push_back
#define eb emplace_back
#define sz(x) (int)(x).size()
#define all(x) begin(x),end(x)
#define FOR(i,l,r) for(int i=(l);i<=(r);i++)
#define ROF(i,r,l) for(int i=(r);i>=(l);i--)

auto& operator<<(auto &o, pair<auto, auto> p) {
	return o << "(" << p.st << ", " << p.nd << ")";}
auto operator<<(auto &o, auto x)->decltype(end(x), o) {
	o << "{"; int i=0; for (auto e : x) o << ","+!i++ << e;
	return o << "}";}

#ifdef LOCAL
#define debug(x...) cerr << "[" #x "]: ", [](auto...$) { \
	((cerr << $ << "; "),...) << endl; }(x)
#else
#define debug(...)
#endif

#define rep(i,a,b) for(int i = a; i < (b); i++)
using pii = pair<int, int>;
using vi = vector<int>;

// https://github.com/kth-competitive-programming/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<ld>> 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 = (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,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;
}

const int N = 50000 + 7;

int n, t;
ld p[N], dp[N];

vd jazda(int l, int r) {
	if (l > r) {
		return {1};
	}
	if (l == r) {
		return vd{1 - p[l], p[l]};
	}

	int m = (l + r) >> 1;
	return conv(jazda(l, m), jazda(m + 1, r));
}

const ld eps = 1e-8;

signed main() {
	cin.tie(0)->sync_with_stdio(0);
	
	cin >> n >> t;
	FOR(i, 1, n)
		cin >> p[i];
	sort(p + 1, p + 1 + n);
	reverse(p + 1, p + 1 + n);

	const int B = 9000;
	while (n - 1 >= t && n >= B && p[n - B / 2] < 0.5)
		n--;
	
	auto P = jazda(1, t - 1);
	FOR(i, 0, t - 1)
		dp[i] = P[i];

	ld ans = 0;
	FOR(i, t, min(n, t + B)) {
		ROF(j, i, 1) {
			dp[j] *= (1 - p[i]);
			dp[j] += p[i] * dp[j - 1];
		}

		dp[0] *= (1 - p[i]);

		ld now = 0;
		FOR(j, 0, i) if (2 * j - i >= t) {
			now += dp[j];
		}	

		if (ans < now) {
			ans = now;
		}
	}

	rep(i, 0, N)
		dp[i] = 0;

	int l = max(t, n - B);
	P = jazda(1, l - 1);
	FOR(i, 0, l - 1)
		dp[i] = P[i];

	FOR(i, l, n) {
		ROF(j, i, 1) {
			dp[j] *= (1 - p[i]);
			dp[j] += p[i] * dp[j - 1];
		}

		dp[0] *= (1 - p[i]);

		ld now = 0;
		FOR(j, 0, i) if (2 * j - i >= t) {
			now += dp[j];
		}	

		if (ans < now) {
			ans = now;
		}
	}

	cout << fixed << setprecision(9) << ans << '\n';

	return 0;
}