1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
#include <bits/stdc++.h>
using namespace std;

#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define all(x) begin(x), end(x)
#define sz(x) int((x).size())
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;

#ifdef LOCAL
auto operator<<(auto& o, auto x) -> decltype(x.first, o);
auto operator<<(auto& o, auto x) -> decltype(x.end(), o) {
  o << "{";
  for (int i = 0; auto y : x) o << ", " + !i++ * 2 << y;
  return o << "}"; }
auto operator<<(auto& o, auto x) -> decltype(x.first, o) {
  return o << "(" << x.first << ", " << x.second << ")"; }
void __print(auto... x) { ((cerr << x << " "), ...) << endl; }
#define debug(x...) __print("[" #x "]:", x)
#else
#define debug(...) 2137
#endif

const int N = 55555;
const int K = 3000;
int n, t;
double p[N];
double dp[2][N];

int 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);
  dp[0][0] = 1;
  int s = 0;
  double odp = 0;
  rep(i, 0, n) {
    rep(j, s, s + K) {
      dp[1][j + 1] += dp[0][j] * p[i];
      dp[1][j] += dp[0][j] * (1 - p[i]);
    }
    while (s + K - 1 < n && dp[1][s + K] > dp[1][s]) s++;
    while (s > 0 && dp[1][s - 1] > dp[1][s + K - 1]) s--;
    rep(j, max(0, s - 1), s + K + 1) dp[0][j] = exchange(dp[1][j], 0);
    int lim = (t + i + 1 + 1) / 2;
    double ter = 0;
    rep(j, max(s, lim), s + K) ter += dp[0][j];
    odp = max(odp, ter);
  }
  cout << fixed << setprecision(10) << odp << '\n';
}