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#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2446" #define ERROR 1e-7 #include "../../math/and_or_convolution.hpp" #include <bits/stdc++.h> using namespace std; int main() { ll n, m; cin >> n >> m; vll a(n), p(n); for (ll i : rep(n)) cin >> a[i]; for (ll i : rep(n)) cin >> p[i]; vll x(pw(n)); for (ll i : rep(pw(n))) { ll l = 1; for (ll j : rep(n)) { if ((i >> j) & 1) { if (l) { ll d = l / gcd(l, a[j]); l = (__int128_t)d * a[j] > m ? 0 : d * a[j]; } } } if (l) x[i] = m / l; } fzt_super(x); fmt_super(x); fzt_sub(x); fmt_sub(x); fmt_sub(x); double ans = 0; for (ll i : rep(pw(n))) { double q = 1; for (ll j : rep(n)) { if ((i >> j) & 1) { q *= p[j] / 100.0; } else { q *= (1 - p[j] / 100.0); } } x[i] = m - abs(x[i]); ans += x[i] * q; }; cout << ans << endl; }
#line 1 "test/judge.u-aizu.ac.jp/Enumeration.0.test.cpp" #define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2446" #define ERROR 1e-7 #line 2 "math/and_or_convolution.hpp" #line 2 "template.hpp" #include <bits/stdc++.h> using namespace std; #define all(a) begin(a), end(a) #define rall(a) rbegin(a), rend(a) #define uniq(a) (a).erase(unique(all(a)), (a).end()) #define t0 first #define t1 second using ll = long long; using ull = unsigned long long; using pll = pair<ll, ll>; using vll = vector<ll>; constexpr double pi = 3.14159265358979323846; constexpr ll dy[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0}; constexpr ll dx[9] = {1, 0, -1, 0, 1, -1, -1, 1, 0}; constexpr ll sign(ll a) { return (a > 0) - (a < 0); } constexpr ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); } constexpr ll cdiv(ll a, ll b) { return -fdiv(-a, b); } constexpr ll pw(ll n) { return 1ll << n; } constexpr ll flg(ll n) { return 63 - __builtin_clzll(n); } constexpr ll clg(ll n) { return n == 1 ? 0 : flg(n - 1) + 1; } constexpr ll safemod(ll x, ll mod) { return (x % mod + mod) % mod; } template <typename T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>; template <typename T> constexpr T sq(const T &a) { return a * a; } template <typename T, typename U> constexpr bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; } template <typename T, typename U> constexpr bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; } template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &a) { os << "(" << a.first << ", " << a.second << ")"; return os; } template <typename T, typename U, typename V> ostream &operator<<(ostream &os, const tuple<T, U, V> &a) { os << "(" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a) << ")"; return os; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &a) { os << "("; for (auto itr = a.begin(); itr != a.end(); ++itr) os << *itr << (next(itr) != a.end() ? ", " : ""); os << ")"; return os; } template <typename T> ostream &operator<<(ostream &os, const set<T> &a) { os << "("; for (auto itr = a.begin(); itr != a.end(); ++itr) os << *itr << (next(itr) != a.end() ? ", " : ""); os << ")"; return os; } template <typename T> ostream &operator<<(ostream &os, const multiset<T> &a) { os << "("; for (auto itr = a.begin(); itr != a.end(); ++itr) os << *itr << (next(itr) != a.end() ? ", " : ""); os << ")"; return os; } template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &a) { os << "("; for (auto itr = a.begin(); itr != a.end(); ++itr) os << *itr << (next(itr) != a.end() ? ", " : ""); os << ")"; return os; } #ifdef ONLINE_JUDGE #define dump(...) (void(0)) #else void debug() { cerr << endl; } template <typename Head, typename... Tail> void debug(Head &&head, Tail &&... tail) { cerr << head; if (sizeof...(Tail)) cerr << ", "; debug(tail...); } #define dump(...) cerr << __LINE__ << ": " << #__VA_ARGS__ << " = ", debug(__VA_ARGS__) #endif struct rep { struct itr { ll v; itr(ll v) : v(v) {} void operator++() { ++v; } ll operator*() const { return v; } bool operator!=(itr i) const { return v < *i; } }; ll l, r; rep(ll l, ll r) : l(l), r(r) {} rep(ll r) : rep(0, r) {} itr begin() const { return l; }; itr end() const { return r; }; }; struct per { struct itr { ll v; itr(ll v) : v(v) {} void operator++() { --v; } ll operator*() const { return v; } bool operator!=(itr i) const { return v > *i; } }; ll l, r; per(ll l, ll r) : l(l), r(r) {} per(ll r) : per(0, r) {} itr begin() const { return r - 1; }; itr end() const { return l - 1; }; }; struct io_setup { static constexpr int PREC = 20; io_setup() { cout << fixed << setprecision(PREC); cerr << fixed << setprecision(PREC); }; } iOS; #line 2 "math/fzt_fmt.hpp" #line 4 "math/fzt_fmt.hpp" template <typename V> void fzt_super(vector<V> &a) { for (ll i : rep(flg(a.size()))) { for (ll s : rep(a.size())) { if ((s >> i) & 1) a[s ^ pw(i)] += a[s]; } } } template <typename V> void fzt_sub(vector<V> &a) { for (ll i : rep(flg(a.size()))) { for (ll s : rep(a.size())) { if (!((s >> i) & 1)) a[s ^ pw(i)] += a[s]; } } } template <typename V> void fmt_super(vector<V> &a) { for (ll i : rep(flg(a.size()))) { for (ll s : rep(a.size())) { if ((s >> i) & 1) a[s ^ pw(i)] -= a[s]; } } } template <typename V> void fmt_sub(vector<V> &a) { for (ll i : rep(flg(a.size()))) { for (ll s : rep(a.size())) { if (!((s >> i) & 1)) a[s ^ pw(i)] -= a[s]; } } } #line 5 "math/and_or_convolution.hpp" template <typename V> vector<V> and_convolution(vector<V> a, vector<V> b) { ll _n = max(a.size(), b.size()), n; for (n = 1; n < _n; n <<= 1) {} a.resize(n), b.resize(n); fzt_super(a), fzt_super(b); for (ll i : rep(n)) a[i] *= b[i]; fmt_super(a); return a; } template <typename V> vector<V> or_convolution(vector<V> a, vector<V> b) { ll _n = max(a.size(), b.size()), n; for (n = 1; n < _n; n <<= 1) {} a.resize(n), b.resize(n); fzt_sub(a), fzt_sub(b); for (ll i : rep(n)) a[i] *= b[i]; fmt_sub(a); return a; } #line 4 "test/judge.u-aizu.ac.jp/Enumeration.0.test.cpp" #line 6 "test/judge.u-aizu.ac.jp/Enumeration.0.test.cpp" using namespace std; int main() { ll n, m; cin >> n >> m; vll a(n), p(n); for (ll i : rep(n)) cin >> a[i]; for (ll i : rep(n)) cin >> p[i]; vll x(pw(n)); for (ll i : rep(pw(n))) { ll l = 1; for (ll j : rep(n)) { if ((i >> j) & 1) { if (l) { ll d = l / gcd(l, a[j]); l = (__int128_t)d * a[j] > m ? 0 : d * a[j]; } } } if (l) x[i] = m / l; } fzt_super(x); fmt_super(x); fzt_sub(x); fmt_sub(x); fmt_sub(x); double ans = 0; for (ll i : rep(pw(n))) { double q = 1; for (ll j : rep(n)) { if ((i >> j) & 1) { q *= p[j] / 100.0; } else { q *= (1 - p[j] / 100.0); } } x[i] = m - abs(x[i]); ans += x[i] * q; }; cout << ans << endl; }