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
#include <bits/stdc++.h>

using i64 = long long;
using u64 = unsigned long long;
using u32 = unsigned;
using u128 = unsigned __int128;

constexpr int B = 670;

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    
    int n, t;
    std::cin >> n >> t;
    
    std::vector<double> p(n);
    for (int i = 0; i < n; i++) {
        std::string s;
        std::cin >> s;
        p[i] = std::stod(s);
    }
    
    std::sort(p.begin(), p.end(), std::greater());
    
    std::vector<double> dp(n + 1);
    dp[0] = 1;
    
    double ans = 0;
    
    double sum = 0;
    
    for (int i = 0; i < n; i++) {
        int L = std::max(0, int(sum - B));
        int R = std::min(i, int(sum + B));
        for (int j = R; j >= L; j--) {
            dp[j + 1] += dp[j] * p[i];
            dp[j] *= (1 - p[i]);
        }
        dp[L] += p[i];
        if (i + 1 >= t) {
            ans = std::max(ans, dp[(i + 2 + t) / 2]);
        }
        sum += p[i];
    }
    
    std::cout << std::fixed << std::setprecision(10) << ans << "\n";
    
    return 0;
}