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#include <vector>
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#ifdef LOCAL
#include "../debug/debug.h"
#else
#define debug(...)
#define debugArr(...)
#endif

using namespace std;
using namespace __gnu_pbds;

using ll = long long;
using db = double;
using pi = pair<int,int>;
using pl = pair<ll,ll>;
using vi = vector<int>;
using vl = vector<ll>;
using vb = vector<bool>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vvi = vector<vi>;

#define mp make_pair
#define eb emplace_back
#define pb push_back
#define x first
#define y second
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(), (x).rend() 
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define per(i,a,b) for(int i=(b)-1;i>=(a);i--)
#define ft front()
#define bk back()
#define rsz resize
#define ins insert
#define each(a,x) for(auto&a:x)

template<class T> bool ckmin(T& a, T b) { return b<a?a=b,1:0; }
template<class T> bool ckmax(T& a, T b) { return b>a?a=b,1:0; }
template<class T> int lwb(vector<T>& a, const T& b) { return int(lower_bound(all(a),b)-bg(a)); }
template<class T> int upb(vector<T>& a, const T& b) { return int(upper_bound(all(a),b)-bg(a)); }
template<class T> void remdup(vector<T>& v) { sort(all(v)); v.erase(unique(all(v)),end(v)); }

constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bitlog(int x) { return x == 0 ? 0 : 31 - __builtin_clz(x); }
constexpr int pct(ll x) { return __builtin_popcountll(x); }
constexpr int bitlog(ll x) { return x == 0 ? 0 : 63 - __builtin_clzll(x); }

constexpr ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); }  // divide a by b rounded up
constexpr ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); }  // divide a by b rounded down
constexpr int cdiv(int a, int b) { return a / b + ((a ^ b) > 0 && a % b); }  // divide a by b rounded down
constexpr int fdiv(int a, int b) { return a / b - ((a ^ b) < 0 && a % b); }  // divide a by b rounded down

const pi MOVES[] = {{-1, 0}, {0, -1}, {1, 0}, {0, 1}};

#ifdef LOCAL
mt19937_64 rng(0xabadbeef);
#else
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
#endif

ll randr(ll l, ll r) { return uniform_int_distribution<ll>(l, r)(rng); }

const int N = 5e4+8;
const int B = 200;

db p[N];
db dp[2][2*N];
int n, t;

const db EPS = 1e-18;

signed main() {
    cin.tie(0)->sync_with_stdio(0);

    cin >> n >> t;
    rep(i,0,n) cin >> p[i];
    sort(p, p + n);
    reverse(p, p + n);

    db res = 0.0;
    db ev = 0.0;

    dp[1][N] = 1.0;

    int l = N;
    int r = N;

    rep(i,0,n) {
        int nxt = i & 1;
        int prv = nxt ^ 1;

        l--; r++;

        rep(j,l,r+1) {
            dp[nxt][j] = dp[prv][j-1] * p[i] + dp[prv][j+1] * (1.0 - p[i]);
        }

        ev += 2 * p[i] - 1;
        int int_ev = N + (int)ev;

        while (int_ev - l > B && dp[nxt][l] < EPS && dp[nxt][l+1] < EPS) {
            dp[nxt][l] = 0;
            l++;
        }
        while (r - int_ev > B && dp[nxt][r] < EPS && dp[nxt][r-1] < EPS) {
            dp[nxt][r] = 0;
            r--;
        }

        db cur = 0;
        rep(j, max(N+t, l), r+1) {
            cur += dp[nxt][j];
        }

        ckmax(res, cur);
    }

    cout << fixed << setprecision(10) << res << '\n';

    return 0;
}