#line 1 "library-cpp/other/template.hpp"
// clang-format off
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
template <class T> using maxheap = priority_queue<T>;
template <class T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T> using vec = vector<T>;
template <class T> using vvec = vector<vector<T>>;
#define OVERLOAD_REP(_1, _2, _3, name, ...) name
#define REP0(n) for (auto minato = decay_t<decltype(n)>{}; minato < (n); ++minato)
#define REP1(i, n) for (auto i = decay_t<decltype(n)>{}; (i) < (n); (i)++)
#define REP2(i, l, r) for (auto i = (l); (i) < (r); (i)++)
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1, REP0)(__VA_ARGS__)
#define OVERLOAD_RREP(_1, _2, _3, name, ...) name
#define RREP1(i, n) for (auto i = (n) - 1; (i) >= decay_t<decltype(n)>{}; (i)--)
#define RREP2(i, l, r) for (auto i = (r) - 1; (i) >= (l); (i)--)
#define rrep(...) OVERLOAD_RREP(__VA_ARGS__, RREP2, RREP1)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
template <class Container> int SZ(const Container& v) { return int(v.size()); }
template <class T> void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }
template <class T> T MAX(const vector<T>& v) { return *max_element(v.begin(), v.end()); }
template <class T> T MIN(const vector<T>& v) { return *min_element(v.begin(), v.end()); }
template <class T> T SUM(const vector<T>& v) { return accumulate(v.begin(), v.end(), T(0)); }
template <class T> T ABS(T x) { return max(x, -x); }
template <class T1, class T2> bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; }
template <class T1, class T2> bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; }
int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }
int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); }
int popcount(ull x) { return __builtin_popcountll(x); }
int kthbit(ull x, int k) { return (x >> k) & 1; }
constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x - 1) * 10; }
template <typename S> void rearrange(const vector<S>& id) { (void)id; }
template <typename S, typename T> void rearrange_exec(const vector<S>& id, vector<T>& v) { vector<T> w(v.size()); for (size_t i = 0; i < id.size(); i++) { w[i] = v[id[i]]; } v.swap(w); }
template <typename S, typename Head, typename... Tail> void rearrange(const vector<S>& id, Head& a, Tail& ...tail) { rearrange_exec(id, a); rearrange(id, tail...); }
istream& operator>>(istream& is, __int128_t& x) {
    x = 0;
    string s;
    is >> s;
    int n = int(s.size()), it = 0;
    if (s[0] == '-') it++;
    for (; it < n; it++) x = (x * 10 + s[it] - '0');
    if (s[0] == '-') x = -x;
    return is;
}
ostream& operator<<(ostream& os, __int128_t x) {
    if (x == 0) return os << 0;
    if (x < 0) os << '-', x = -x;
    deque<int> deq;
    while (x) deq.emplace_front(x % 10), x /= 10;
    for (int e : deq) os << e;
    return os;
}
template <class T> vector<T> &operator++(vector<T>& v) { for (auto& e : v) { e++; } return v;} 
template <class T> vector<T> operator++(vector<T>& v, int) { auto res = v; for (auto& e : v) { e++; } return res; }
template <class T> vector<T> &operator--(vector<T>& v) { for (auto& e : v) { e--; } return v; }
template <class T> vector<T> operator--(vector<T>& v, int) { auto res = v; for (auto& e : v) { e--; } return res; }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x) { return pair<T1, T2>(-x.first, -x.second); }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first - y.first, x.second - y.second); }
template <class T1, class T2> pair<T1, T2> operator+(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first + y.first, x.second + y.second); }
template <class T1, class T2> pair<T1, T2> operator+=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l + r; }
template <class T1, class T2> pair<T1, T2> operator-=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l - r; }
constexpr char ln = '\n';
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
void YES(bool t = true) { cout << YESNO[t] << "\n"; }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = true) { cout << YesNo[t] << "\n"; }
void No(bool t = 1) { Yes(!t); }
template <class T> void drop(T x) { cout << x << "\n"; exit(0); }
#define INT(...)     \
    int __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LL(...)     \
    ll __VA_ARGS__; \
    IN(__VA_ARGS__)
#define STR(...)        \
    string __VA_ARGS__; \
    IN(__VA_ARGS__)
#define CHR(...)      \
    char __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LDB(...)             \
    long double __VA_ARGS__; \
    IN(__VA_ARGS__)
#define VEC(type, name, size) \
    vector<type> name(size);  \
    IN(name)
#define VEC2(type, name1, name2, size)     \
    vector<type> name1(size), name2(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i])
#define VEC3(type, name1, name2, name3, size)           \
    vector<type> name1(size), name2(size), name3(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i])
#define VEC4(type, name1, name2, name3, name4, size)                 \
    vector<type> name1(size), name2(size), name3(size), name4(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]);
#define VV(type, name, N, M)                       \
    vector<vector<type>> name(N, vector<type>(M)); \
    IN(name)
template <class T> void scan(T& a) { cin >> a; }
template <class T> void scan(vector<T>& a) { for (auto& i : a) scan(i); }
void IN() {}
template <class Head, class... Tail> void IN(Head& head, Tail&... tail) { scan(head); IN(tail...); }
void print() { cout << "\n"; }
template <class T> void print(const vector<T>& v) { for (auto it = v.begin(); it != v.end(); ++it) { if (it != v.begin()) { cout << " "; } cout << *it; } print(); }
template <class T, class... Args> void print(const T& x, const Args& ... args) { cout << x; if (sizeof...(Args)) cout << " "; print(args...); }
#ifdef MINATO_LOCAL
template <class T1, class T2> ostream& operator<<(ostream& os, pair<T1, T2> p) { return os << "(" << p.first << ", " << p.second << ")"; }
template <size_t N, class TUPLE> void debug_tuple(ostream& os, TUPLE _) { (void)os; (void)_; }
template <size_t N, class TUPLE, class T, class ...Args> void debug_tuple(ostream &os, TUPLE t) { os << (N == 0 ? "" : ", ") << get<N>(t); debug_tuple<N + 1, TUPLE, Args...>(os, t); }
template <class ...Args> ostream& operator<<(ostream& os, tuple<Args...> t) { os << "("; debug_tuple<0, tuple<Args...>, Args...>(os, t); return os << ")"; }
string debug_delim(int& i) { return i++ == 0 ? "" : ", "; }
#define debug_embrace(x) { int i = 0; os << "{";  { x } return os << "}"; }
template <class T> ostream& operator<<(ostream& os, vector<T> v) { debug_embrace( for (T e : v) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> ostream& operator<<(ostream& os, array<T, N> a) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> enable_if_t<!is_same_v<char, remove_cv_t<T>>, ostream>& operator<<(ostream& os, T(&a)[N]) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class Key> ostream& operator<<(ostream& os, set<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class Key, class T> ostream& operator<<(ostream& os, map<Key, T> mp) { debug_embrace( for (auto e : mp) { os << debug_delim(i) << e; }) }
template <class Key> ostream& operator<<(ostream& os, multiset<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class T> ostream& operator<<(ostream& os, queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.front(); } ) }
template <class T> ostream& operator<<(ostream& os, deque<T> q) { debug_embrace( for (T e : q) { os << debug_delim(i) << e; } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T, vector<T>, greater<T>> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
void debug_out() { cerr << endl; }
template <class T, class... Args> void debug_out(const T& x, const Args& ... args) { cerr << " " << x; debug_out(args...); }
#define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// clang-format on
#line 2 "A.cpp"
void solve() {
    INT(N, M);
    VEC3(int, A, B, P, N);

    vvec<ld> dp(1 << N, vec<ld>(M + 1));
    vvec<int> seen(1 << N, vec<int>(M + 1));
    auto rec = [&](auto self, int mask, int m) -> ld {
        if (seen[mask][m]) return dp[mask][m];
        seen[mask][m] = 1;
        ld ret = 0;
        {
            rep(i, N) {
                if (!kthbit(mask, i)) {
                    ret += 1.0L / A[i];
                } else {
                    ret += 1.0L / B[i];
                }
            }
        }
        if (mask == ((1 << N) - 1) or m == M) return dp[mask][m] = ret;
        rep(i, N) {
            if (kthbit(mask, i)) continue;
            ld p = 1.0L / P[i];
            chmax(ret, p * self(self, mask | (1 << i), m) +
                           (1.0L - p) * self(self, mask, m + 1));
        }
        return dp[mask][m] = ret;
    };
    print(rec(rec, 0, 0));
}

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(7);

    int T = 1;
    // cin >> T;
    for (int test_case = 1; test_case <= T; test_case++) {
        // debug(test_case);
        solve();
    }
}