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#pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
#define fi first
#define se second
#define pn printf("\n")
#define ssize(x) int(x.size())
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define bitcount(x) __builtin_popcount(x)
#define bitcountll(x) __builtin_popcountll(x)
#define clz(x) __builtin_clz(x)
#define ctz(x) __builtin_ctz(x)
#define eb emplace_back
//~ #define r(x) resize(x)
//~ #define rf(x, c) resize(x, c)
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<int, ll> pil;
typedef pair<ll, int> pli;
typedef pair<ll, ll> pll;
typedef double db;
typedef long double ldb;
#define V vector
//~ void read(int &a){
		//~ a = 0; char c = _getchar_nolock();
		//~ while(c<'0'||'9'<c) c = _getchar_nolock();
		//~ while('0'<=c&&c<='9') a = a*10+c-'0', c = _getchar_nolock();
//~ }
// random_device rd;
// mt19937 rng(rd());
// uniform_int_distribution<int> mrandint(1, (1<<30)-1);
// uniform_int_distribution<ll> mrandll(1, 1ll<<60);	
// int randint(){ return mrandint(rng); }
// ll randll(){ return mrandll(rng); }
int inf = 2.1e09; ll infll = 2e18; int mod = (1<<23)*119+1; //1e09+7;
int add(int a, int b){return a+b >= mod ? a+b - mod : a+b;}
int sub(int a, int b){return a-b < 0 ? a-b + mod : a-b;}
int mul(int a, int b){return int(a * ll(b) % mod);}
int fpow(int a, ll b){
	int ret = 1;
	while(b){
		if(b & 1) ret = mul(ret, a);
		b >>= 1, a = mul(a, a);
	} return ret;
}
int inv(int a){ return fpow(a, mod-2); }
int coeff(int n, int k, vector<int> &fac, vector<int> &invfac){
	if(k < 0 || n < k) return 0;
	return mul(fac[n], mul(invfac[n-k], invfac[k]));
}
void calcfac(int n, vector<int> &fac, vector<int> &invfac){
	fac[0] = 1, invfac[0] = 1;
	for(int i = 1; i <= n; ++i) fac[i] = mul(fac[i-1], i);
	invfac[n] = inv(fac[n]);
	for(int i = n-1; i; --i) invfac[i] = mul(invfac[i+1], i+1);
}

struct lz{
	double a = 0, b = 0;
	lz(){}
	lz(double A, double B) : a(A), b(B) {}
	lz operator+(const lz &A) const{return lz(a + A.a, b + A.b);}
	lz operator-(const lz &A) const{return lz(a - A.a, b - A.b);}
	lz operator*(const lz &A) const{return lz(a * A.a - b * A.b, a * A.b + b * A.a);}
	lz operator*(const double &A) const{return lz(a * A, b * A);}
	lz operator/(const double &A) const{return lz(a / A, b / A);}
};

void to_lz(V<lz> &t, V<double> &a){
	t.resize(ssize(a));
	for(int i = 0; i < ssize(a); ++i)
		t[i].a = a[i];
	
}

struct poly{
	const int mxpot = 1<<16; // do zmiany wedle potrzeby
	vector<lz> roots[2];
	void calc_roots(){
		double ang; lz wn;
		roots[0].resize(mxpot), roots[1].resize(mxpot);
		ang = 2*acos(-1)/mxpot, roots[0][0] = lz(1, 0), roots[1][0] = lz(1, 0);
		wn = lz(cos(ang), sin(ang));
		for(int j = 1; j < mxpot; ++j) roots[0][j] = roots[0][j-1] * wn;
		wn = lz(cos(-ang), sin(-ang));
		for(int j = 1; j < mxpot; ++j) roots[1][j] = roots[1][j-1] * wn;
	}
	poly(){ calc_roots(); }
	void odw(int &x, int p){
		int a, b;
		for(int i = 0; i < p>>1; ++i) a = (x&(1<<i)), b = (x&(1<<(p-i-1))), x -= a + b, x += (a<<(p-2*i-1))+(b>>(p-2*i-1));
	}
	void dft(vector<lz> &a, bool inv){
		int n = int(a.size()), p = __builtin_ctz(n), tmp;
		for(int i = 0; i < n; ++i){
			tmp = i, odw(tmp, p);
			if(i < tmp) swap(a[i], a[tmp]);
		}
		int w;
		for(int dl = 2; dl <= n; dl<<=1){
			w = mxpot/dl;
			for(int i = 0; i < n; i += dl){
				for(int k = 0; k < dl>>1; ++k){
					lz A = a[i+k], B = a[i+k+(dl>>1)]*roots[inv][w*k];
					a[i+k] = A + B;
					a[i+k+(dl>>1)] = A - B;
				}
			}
		}
	}
	void fft(vector<lz> &a, vector<lz> &b){
		int n = int(a.size()+b.size()), pot = 1;
		while(pot < n) pot <<= 1;
		// n = pot;
		a.resize(pot), b.resize(pot);
		dft(a, 0), dft(b, 0);
		for(int i = 0; i < pot; ++i) a[i] = a[i] * b[i];
		dft(a, 1);
		for(int i = 0; i < pot; ++i) a[i].a = a[i].a/pot, a[i].b = 0;
        while(n-1 < ssize(a)) a.pop_back();
	}
} multiplier;


void answer(){
	int n, t; cin >> n >> t;
	V<double> p(n);
	for(int i = 0; i < n; ++i) cin >> p[i];
	sort(rall(p));
	int k = int(sqrt(n*16))+1;

	auto get_dp = [&](int l, int r){ // [l, r)
		int N = r-l;
		V<double> dp(N<<1|1, 0), tp(N<<1|1, 0);
		dp[N] = 1;
		for(int i = l; i < r; ++i){
			fill(all(tp), 0);
			for(int j = N-(i-l); j <= N+(i-l); ++j){
				tp[j+1] += dp[j]*p[i];
				tp[j-1] += dp[j]*(1-p[i]);
			}
			dp = tp;
		}
		return dp;
	};
	V<V<double>> dp_list((n+k-1)/k);
	V<V<lz>> lz_dp((n+k-1)/k);
	for(int i = 0; i < n; i += k){
		dp_list[i/k] = get_dp(i, min(n, i+k));
		to_lz(lz_dp[i/k], dp_list[i/k]);
	}
	
	V<lz> dp(1, lz(1, 0));
	int start = 0;
	for(int i = 0; i+1+k <= t; i += k)
		multiplier.fft(dp, lz_dp[i/k]), start += k;


	V<double> dpt(ssize(dp)+2*k), dptmp(ssize(dpt));
	for(int i = 0; i < ssize(dp); ++i)
		dpt[i+k] = dp[i].a;

	double result = 0;
	int mid = ssize(dpt)/2;
	for(int i = start; i < min(n, start+k); ++i){
		fill(all(dptmp), 0);
		for(int j = mid-i; j <= mid+i; ++j){
			dptmp[j+1] += dpt[j]*p[i];
			dptmp[j-1] += dpt[j]*(1-p[i]);
		}
		dpt = dptmp;
		if(t <= i+1){
			double sum = 0;
			for(int j = mid+t; j < ssize(dpt); ++j)
				sum += dpt[j];
			result = max(result, sum);
		}
	}
	multiplier.fft(dp, lz_dp[start/k]);
	start += k;

	for(int I = start; I < n; I += k){
		dpt.resize(2*k, 0), dptmp.resize(2*k, 0);
		mid = ssize(dp)/2;
        double sum = 0;
        for(int j = mid+t; j < ssize(dp); ++j)
            sum += dp[j].a;
		for(int j = mid+t-k; j < min(ssize(dp), mid+t+k-1); ++j)
			dpt[j-(mid+t-k)] = dp[j].a;
		
		for(int i = I; i < min(n, I+k); ++i){
            fill(all(dptmp), 0);
            for(int j = 0; j < 2*k; ++j){
                if(j+1 < 2*k){
                    dptmp[j+1] += dpt[j]*p[i];
                    if(j == k-1)
                        sum += dpt[j]*p[i];
                }
                if(0 <= j-1){
                    dptmp[j-1] += dpt[j]*(1-p[i]);
                    if(j == k)
                        sum -= dpt[j]*(1-p[i]);
                }
            }
            dpt = dptmp;
            result = max(result, sum);
        }
        multiplier.fft(dp, lz_dp[I/k]);
	}
    cout << setprecision(9) << fixed << result << "\n";
}
int main(){
	int T = 1;
	// scanf("%d", &T);
	ios_base::sync_with_stdio(0); cin.tie(0);// cin >> T;
	for(++T; --T; ) answer();
	return 0;
}