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#include <bits/stdc++.h>

#define ll long long
#define ld double
#define endl '\n'
#define st first
#define nd second
#define pb push_back
#define sz(x) (int)(x).size()
#define all(x) (x).begin(), (x).end()
#define FOR(i,l,r) for(int i=(l);i<=(r);i++)
#define ROF(i,r,l) for(int i=(r);i>=(l);i--)
using namespace std;
ll infl=1000000000000000007;
int inf=1000000007;
int mod=998244353;
int mod1=998244353;

#ifdef DEBUG
auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif

const int N=50007,S=500;

ld p[N];
vector<ld>DP[N];

ld DP1[S+7][S+7];


#define rep(i, a, b) for(int i = a; i < (b); ++i)
typedef pair<int, int> pii;
typedef vector<int> vi;
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);
		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 = (double *)&rt[j+k], y = (double *)&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;
}

signed main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int n,t;
    cin>>n>>t;
    FOR(i,1,n) cin>>p[i];
    sort(p+1,p+n+1,greater<ld>());
    DP[0].resize(1);
    DP[0][0]=1;
    FOR(i,1,t%S)
    {
		DP[i].resize(i+1);
		FOR(j,0,i) DP[i][j]=0;
		FOR(j,0,i-1) 
		{
			DP[i][j]+=DP[i-1][j]*(1.0-p[i]);
			DP[i][j+1]+=DP[i-1][j]*p[i];
		}
	}
	int it=t%S;
	ld ans=0;
	//int tt=10;
	while(true)
	{
		debug(it);
		ld T=0;
		FOR(j,(t+it+1)/2,it) T+=DP[it][j];
		ans=max(ans,T);
		//debug(it,DP[it]);
		if(it+S>n)
		{
			FOR(i,max(t,it-S)+1,n)
			{
				DP[i].resize(i+1);
				FOR(j,0,i) DP[i][j]=0;
				FOR(j,0,i-1) 
				{
					DP[i][j]+=DP[i-1][j]*(1.0-p[i]);
					DP[i][j+1]+=DP[i-1][j]*p[i];
				}
				ld act=0;
				FOR(j,(t+i+1)/2,i) act+=DP[i][j];
				ans=max(ans,act);
				debug(i,act);
			}
			break;
		}
		memset(DP1,0,sizeof DP1);
		DP1[0][0]=1;
		FOR(i,1,S)
		{
			FOR(j,0,i-1)
			{
				DP1[i][j]+=DP1[i-1][j]*(1.0-p[it+i]);
				DP1[i][j+1]+=DP1[i-1][j]*p[it+i];
			}
		}
		vector<ld>X(S+1);
		FOR(i,0,S) X[i]=DP1[S][i];
		DP[it+S]=conv(DP[it],X);
		ld T1=0;
		FOR(j,(t+it+S+1)/2,it+S) T1+=DP[it+S][j];
		//cout<<it<<" "<<fixed<<setprecision(7)<<T1<<endl;
		if(it>=t&&T>T1+0.000000001)
		{
			FOR(i,max(t,it-S)+1,it+S)
			{
				DP[i].resize(i+1);
				FOR(j,0,i) DP[i][j]=0;
				FOR(j,0,i-1) 
				{
					DP[i][j]+=DP[i-1][j]*(1.0-p[i]);
					DP[i][j+1]+=DP[i-1][j]*p[i];
				}
				ld act=0;
				FOR(j,(t+i+1)/2,i) act+=DP[i][j];
				ans=max(ans,act);
				debug(i,act);
			}
			break;
		}
		it+=S;
		debug(it);
	}
	cout<<fixed<<setprecision(9)<<ans<<endl;
    
    
    
    return 0;
}