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#include <algorithm>
#include <cmath>
#include <cstdio>
#include <functional>
#include <map>
#include <vector>
using namespace std;

#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define VAR(v,w) __typeof(w) v=(w)
#define SIZE(c) ((int)(c).size())
#define FT first
#define SD second
#define INT(x) int x; scanf("%d", &x)

typedef vector<double> VD;

double p[50000];
map<int, VD> cache;
double res[2][50001];

struct C {
	double re, im;
	C(double re = 0, double im = 0) : re(re), im(im) {}
	C operator+(const C& z) const { return C(re + z.re, im + z.im); }
	C operator-(const C& z) const { return C(re - z.re, im - z.im); }
	C operator*(const C& z) const { return C(re * z.re - im * z.im, re * z.im + im * z.re); }
};

C ac[1 << 17], at[1 << 17], bc[1 << 17], bt[1 << 17], cc[1 << 17], ct[1 << 17];

C rootm(int k, int n) {
	double x = -2 * M_PI * k / n;
	return C(cos(x), sin(x));
}

int round2(int i) {
	int j = 1;
	while (j < i) j <<= 1;
	return j;
}

void fft(C x[], int n, int s, C r[]) {
	if (n == 1) {
		r[0] = x[0];
		return;
	}
	int h = n >> 1;
	int s2 = s << 1;
	fft(x, h, s2, r);
	fft(x + s, h, s2, r + h);
	REP(k,h) {
		C p = r[k];
		C q = rootm(k, n) * r[k + h];
		r[k] = p + q;
		r[k + h] = p - q;
	}
}

void ifft(C x[], int n, C r[]) {
	REP(i,n) x[i].im = -x[i].im;
	fft(x, n, 1, r);
	REP(i,n) r[i].im = -r[i].im;
	REP(i,n) r[i] = r[i] * (1.0L / n);
}

VD conv(const VD& a, const VD& b) {
	if (SIZE(a) < 20 || SIZE(b) < 20 || SIZE(a) + SIZE(b) < 2000) {
		VD c(SIZE(a) + SIZE(b) - 1);
		REP(i,SIZE(a)) REP(j,SIZE(b)) c[i + j] += a[i] * b[j];
		return c;
	}
	int cn = SIZE(a) + SIZE(b) - 1;
	int n = round2(cn);
	REP(i,SIZE(a)) ac[i] = a[i];
	FOR(i,SIZE(a),n) ac[i] = 0;
	REP(i,SIZE(b)) bc[i] = b[i];
	FOR(i,SIZE(b),n) bc[i] = 0;
	fft(ac, n, 1, at);
	fft(bc, n, 1, bt);
	REP(i,n) ct[i] = at[i] * bt[i];
	ifft(ct, n, cc);
	VD c(cn);
	REP(i,cn) c[i] = cc[i].re;
	return c;
}

VD seq(int x, int y, bool save = 0) {
	if (x + 1 == y) return VD{1 - p[x], p[x]};
	if (!x) {
		VAR(it,cache.lower_bound(y));
		if (it != cache.end() && it->FT == y) return it->SD;
		if (it != cache.begin()) {
			--it;
			VD r = conv(it->SD, seq(it->FT, y));
			if (save) cache[y] = r;
			return r;
		}
	}
	int m = (x + y) >> 1;
	VD r = conv(seq(x, m, save), seq(m, y));
	if (save) cache[y] = r;
	return r;
}

double check(int n, int t) {
	VD v = seq(0, n, 1);
	double r = 0;
	FOR(i,(n+t+1)>>1,n+1) r += v[i];
	return r;
}

double scan(int start, int end, int t) {
	VD ss = seq(0, start, 1);
	REP(j,start+1) res[start & 1][j] = ss[j];
	double best = 0;
	FOR(j,(start+t+1)>>1,start+1) best += res[start & 1][j];
	FOR(i,start+1,end+1) {
		REP(j,i+1) {
			res[i & 1][j] = 0;
			if (j) res[i & 1][j] = res[(i + 1) & 1][j - 1] * p[i - 1];
			if (j < i) res[i & 1][j] += res[(i + 1) & 1][j] * (1 - p[i - 1]);
		}
		double res1 = 0;
		FOR(j,(i+t+1)>>1,i+1) res1 += res[i & 1][j];
		best = max(best, res1);
	}
	return best;
}

int main() {
	INT(n);
	INT(t);
	REP(i,n) {
		double pp;
		scanf("%lf", &pp);
		p[i] = pp;
	}
	sort(p, p + n, greater<double>());
	int d = (n + 1 - t) >> 1;
	int a = 0;
	int b = d - 1;
	while (a + 1000 < b) {
		int m1 = ((a << 1) + b) / 3;
		int m2 = (a + (b << 1)) / 3;
		if (check(t + (m1 << 1), t) < check(t + (m2 << 1), t))
			a = m1;
		else
			b = m2;
	}
	double r = max(r, scan(t + (a << 1), t + (b << 1), t));
	d = (n - t) >> 1;
	a = 0;
	b = d - 1;
	while (a + 1000 < b) {
		int m1 = ((a << 1) + b) / 3;
		int m2 = (a + (b << 1)) / 3;
		if (check(t  + (m1 << 1) + 1, t) < check(t + (m2 << 1) + 1, t))
			a = m1;
		else
			b = m2;
	}
	r = max(r, scan(t + (a << 1) + 1, t + (b << 1) + 1, t));
	printf("%.9f\n", r);
}