結果
| 問題 | No.472 平均順位 |
| ユーザー |
 taotao54321
|
| 提出日時 | 2019-08-17 00:20:11 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
MLE
|
| 実行時間 | - |
| コード長 | 22,313 bytes |
| コンパイル時間 | 2,174 ms |
| コンパイル使用メモリ | 212,740 KB |
| 実行使用メモリ | 590,208 KB |
| 最終ジャッジ日時 | 2024-09-23 05:19:45 |
| 合計ジャッジ時間 | 5,403 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,816 KB |
| testcase_01 | AC | 2 ms
6,940 KB |
| testcase_02 | AC | 2 ms
6,944 KB |
| testcase_03 | AC | 2 ms
6,940 KB |
| testcase_04 | AC | 2 ms
6,944 KB |
| testcase_05 | AC | 2 ms
6,940 KB |
| testcase_06 | AC | 2 ms
6,944 KB |
| testcase_07 | AC | 2 ms
6,940 KB |
| testcase_08 | AC | 5 ms
6,944 KB |
| testcase_09 | AC | 20 ms
19,200 KB |
| testcase_10 | AC | 13 ms
13,312 KB |
| testcase_11 | AC | 57 ms
53,248 KB |
| testcase_12 | AC | 41 ms
38,400 KB |
| testcase_13 | AC | 151 ms
134,272 KB |
| testcase_14 | MLE | - |
| testcase_15 | AC | 155 ms
134,144 KB |
| testcase_16 | MLE | - |
| testcase_17 | MLE | - |
| testcase_18 | AC | 38 ms
37,504 KB |
| testcase_19 | AC | 76 ms
65,792 KB |
ソースコード
/**
*
*/
// header {{{
#include <bits/stdc++.h>
using namespace std;
#define CPP_STR(x) CPP_STR_I(x)
#define CPP_CAT(x,y) CPP_CAT_I(x,y)
#define CPP_STR_I(args...) #args
#define CPP_CAT_I(x,y) x ## y
#define SFINAE(pred...) std::enable_if_t<(pred), std::nullptr_t> = nullptr
#define ASSERT(expr...) assert((expr))
using i8 = int8_t;
using u8 = uint8_t;
using i16 = int16_t;
using u16 = uint16_t;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using f32 = float;
using f64 = double;
using f80 = __float80;
// }}}
constexpr i64 INF = INT64_C(1'010'000'000'000'000'017);
constexpr f64 FINF = 1e100;
constexpr i64 MOD = INT64_C(1'000'000'007);
constexpr f64 EPS = 1e-12;
constexpr f64 PI = 3.14159265358979323846;
// util {{{
#define FOR(i, start, end) for(i64 i = (start), CPP_CAT(i,xxxx_end)=(end); i < CPP_CAT(i,xxxx_end); ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(f,c,...) (([&](decltype((c)) cccc) { return (f)(std::begin(cccc), std::end(cccc), ## __VA_ARGS__); })(c))
#define LIFT(f) ([](auto&&... args) -> decltype(auto) { return (f)(std::forward<decltype(args)>(args)...); })
template<typename C>
constexpr i64 SIZE(const C& c) noexcept { return static_cast<i64>(c.size()); }
template<typename T, size_t N>
constexpr i64 SIZE(const T (&)[N]) noexcept { return static_cast<i64>(N); }
template<typename T, typename U, typename Comp=less<>>
constexpr bool chmax(T& xmax, const U& x, Comp comp={}) noexcept {
if(comp(xmax, x)) {
xmax = x;
return true;
}
return false;
}
template<typename T, typename U, typename Comp=less<>>
constexpr bool chmin(T& xmin, const U& x, Comp comp={}) noexcept {
if(comp(x, xmin)) {
xmin = x;
return true;
}
return false;
}
template<typename BinaryFunc, typename UnaryFunc>
auto ON(BinaryFunc&& bf, UnaryFunc&& uf) {
return [bf=forward<BinaryFunc>(bf),uf=forward<UnaryFunc>(uf)](const auto& x, const auto& y) {
return bf(uf(x), uf(y));
};
}
template<typename F>
auto LT_ON(F&& f) {
return ON(less<>{}, forward<F>(f));
}
template<typename F>
auto GT_ON(F&& f) {
return ON(greater<>{}, forward<F>(f));
}
template<typename F>
auto EQ_ON(F&& f) {
return ON(equal_to<>{}, forward<F>(f));
}
template<typename F>
auto NE_ON(F&& f) {
return ON(not_equal_to<>{}, forward<F>(f));
}
// tuple {{{
template<i64 I=0, typename F, typename... TS, SFINAE(sizeof...(TS) == I)>
void tuple_enumerate(tuple<TS...>&, F&&) {}
template<i64 I=0, typename F, typename... TS, SFINAE(sizeof...(TS) > I)>
void tuple_enumerate(tuple<TS...>& t, F&& f) {
f(I, get<I>(t));
tuple_enumerate<I+1>(t, forward<F>(f));
}
template<i64 I=0, typename F, typename... TS, SFINAE(sizeof...(TS) == I)>
void tuple_enumerate(const tuple<TS...>&, F&&) {}
template<i64 I=0, typename F, typename... TS, SFINAE(sizeof...(TS) > I)>
void tuple_enumerate(const tuple<TS...>& t, F&& f) {
f(I, get<I>(t));
tuple_enumerate<I+1>(t, forward<F>(f));
}
// }}}
// container {{{
template<typename T> struct is_container : false_type {};
template<typename T, size_t N> struct is_container<array<T,N>> : true_type {};
template<typename... Args> struct is_container<vector<Args...>> : true_type {};
template<typename... Args> struct is_container<deque<Args...>> : true_type {};
template<typename... Args> struct is_container<list<Args...>> : true_type {};
template<typename... Args> struct is_container<forward_list<Args...>> : true_type {};
template<typename... Args> struct is_container<set<Args...>> : true_type {};
template<typename... Args> struct is_container<multiset<Args...>> : true_type {};
template<typename... Args> struct is_container<unordered_set<Args...>> : true_type {};
template<typename... Args> struct is_container<unordered_multiset<Args...>> : true_type {};
template<typename... Args> struct is_container<map<Args...>> : true_type {};
template<typename... Args> struct is_container<multimap<Args...>> : true_type {};
template<typename... Args> struct is_container<unordered_map<Args...>> : true_type {};
template<typename... Args> struct is_container<unordered_multimap<Args...>> : true_type {};
template<typename T, typename Enable=void>
struct ProconHash {
size_t operator()(const T& x) const noexcept {
return hash<T>{}(x);
}
};
template<typename T>
size_t procon_hash_value(const T& x) noexcept {
return ProconHash<T>{}(x);
}
size_t procon_hash_combine(size_t h1, size_t h2) noexcept {
constexpr size_t M = UINT64_C(0xc6a4a7935bd1e995);
constexpr int R = 47;
h2 *= M;
h2 ^= h2 >> R;
h2 *= M;
h1 ^= h2;
h1 *= M;
h1 += 0xe6546b64;
return h1;
}
template<typename T1, typename T2>
struct ProconHash<pair<T1,T2>> {
size_t operator()(const pair<T1,T2>& p) const noexcept {
size_t h1 = procon_hash_value(p.first);
size_t h2 = procon_hash_value(p.second);
return procon_hash_combine(h1, h2);
}
};
template<typename... TS>
struct ProconHash<tuple<TS...>> {
size_t operator()(const tuple<TS...>& t) const noexcept {
size_t h = 0;
tuple_enumerate(t, [&h](const auto& e) {
h = procon_hash_combine(h, procon_hash_value(e));
});
return h;
}
};
template<typename C>
struct ProconHash<C,enable_if_t<is_container<C>::value>> {
size_t operator()(const C& c) const noexcept {
size_t h = 0;
for(const auto& e : c)
h = procon_hash_combine(h, procon_hash_value(e));
return h;
}
};
template<typename T, typename Hash=ProconHash<T>, typename Eq=equal_to<T>>
using HashSet = unordered_set<T,Hash,Eq>;
template<typename K, typename V, typename Hash=ProconHash<K>, typename Eq=equal_to<K>>
using HashMap = unordered_map<K,V,Hash,Eq>;
template<typename T, typename Hash=ProconHash<T>, typename Eq=equal_to<T>>
using HashMultiset = unordered_multiset<T,Hash,Eq>;
template<typename K, typename V, typename Hash=ProconHash<K>, typename Eq=equal_to<K>>
using HashMultimap = unordered_multimap<K,V,Hash,Eq>;
template<typename T>
auto vec_make(i64 n, T x) {
return vector<T>(n, x);
}
template<typename T, typename... Args, SFINAE(sizeof...(Args) >= 2)>
auto vec_make(i64 n, Args... args) {
auto inner = vec_make<T>(args...);
return vector<decltype(inner)>(n, inner);
}
template<typename T>
auto vec_reserve(i64 cap) {
vector<T> res;
res.reserve(cap);
return res;
}
template<typename T=i64>
auto vec_iota(i64 n, T init={}) {
vector<i64> res(n);
ALL(iota, res, init);
return res;
}
template<typename T, typename Comp, typename Cont=vector<T>>
auto priority_queue_make(const Comp& comp, Cont&& cont={}) {
return priority_queue<T,remove_reference_t<Cont>,Comp>(comp, forward<Cont>(cont));
}
template<typename T, typename Comp>
auto priority_queue_reserve(const Comp& comp, i64 cap) {
return priority_queue<T,vector<T>,Comp>(comp, vec_reserve<T>(cap));
}
template<typename T, size_t N, size_t... NS>
struct ArrayType {
using type = array<typename ArrayType<T,NS...>::type,N>;
};
template<typename T, size_t N>
struct ArrayType<T,N> {
using type = array<T,N>;
};
template<typename T, size_t... NS>
using Array = typename ArrayType<T,NS...>::type;
template<typename T, size_t N>
T& array_at(Array<T,N>& ary, i64 i) {
return ary[i];
}
template<typename T, size_t N, size_t... NS, typename... Args>
T& array_at(Array<T,N,NS...>& ary, i64 i, Args... args) {
return array_at<T,NS...>(ary[i], args...);
}
template<typename T, size_t N>
const T& array_at(const Array<T,N>& ary, i64 i) {
return ary[i];
}
template<typename T, size_t N, size_t... NS, typename... Args>
const T& array_at(const Array<T,N,NS...>& ary, i64 i, Args... args) {
return array_at<T,NS...>(ary[i], args...);
}
template<typename T, typename C>
T POP(stack<T,C>& stk) {
T x = stk.top(); stk.pop();
return x;
}
template<typename T, typename C>
T POP(queue<T,C>& que) {
T x = que.front(); que.pop();
return x;
}
template<typename T, typename C, typename Comp>
T POP(priority_queue<T,C,Comp>& que) {
T x = que.top(); que.pop();
return x;
}
// }}}
// fixpoint {{{
template<typename F>
class FixPoint {
public:
explicit constexpr FixPoint(F&& f) : f_(forward<F>(f)) {}
template<typename... Args>
constexpr decltype(auto) operator()(Args&&... args) const {
return f_(*this, forward<Args>(args)...);
}
private:
F f_;
};
template<typename F>
constexpr decltype(auto) FIX(F&& f) {
return FixPoint<F>(forward<F>(f));
}
template<typename F, size_t... NS>
class FixPointMemo {
public:
explicit FixPointMemo(F&& f) : f_(forward<F>(f)) {}
template<typename... Args>
decltype(auto) operator()(Args... args) const {
using R = decltype(f_(*this,args...));
static Array<bool,NS...> done {};
static Array<R,NS...> memo;
if(!array_at<bool,NS...>(done,args...)) {
array_at<R,NS...>(memo,args...) = f_(*this,args...);
array_at<bool,NS...>(done,args...) = true;
}
return array_at<R,NS...>(memo,args...);
}
private:
F f_;
};
template<size_t... NS, typename F>
decltype(auto) FIXMEMO(F&& f) {
return FixPointMemo<F,NS...>(forward<F>(f));
}
// }}}
// string {{{
auto str_reserve(i64 cap) {
string res;
res.reserve(cap);
return res;
}
// }}}
// input {{{
template<typename T, typename Enable=void>
struct Scan {
static T scan(istream& in) {
T res;
in >> res;
return res;
}
};
template<typename T, typename Enable=void>
struct Scan1;
template<typename T>
struct Scan1<T,enable_if_t<is_integral<T>::value && !is_same<T,bool>::value>> {
static T scan1(istream& in) {
return Scan<T>::scan(in) - 1;
}
};
template<typename T1, typename T2>
struct Scan<pair<T1,T2>> {
static pair<T1,T2> scan(istream& in) {
T1 x = Scan<T1>::scan(in);
T2 y = Scan<T2>::scan(in);
return {x,y};
}
};
template<typename T1, typename T2>
struct Scan1<pair<T1,T2>> {
static pair<T1,T2> scan1(istream& in) {
T1 x = Scan1<T1>::scan1(in);
T2 y = Scan1<T2>::scan1(in);
return {x,y};
}
};
template<typename... TS>
struct Scan<tuple<TS...>> {
static tuple<TS...> scan(istream& in) {
return scan_impl<0>(in);
}
private:
template<i64 I, SFINAE(sizeof...(TS) == I)>
static auto scan_impl(istream&) {
return make_tuple();
}
template<i64 I, SFINAE(sizeof...(TS) > I)>
static auto scan_impl(istream& in) {
using T = tuple_element_t<I,tuple<TS...>>;
auto head = make_tuple(Scan<T>::scan(in));
return tuple_cat(head, scan_impl<I+1>(in));
}
};
template<typename... TS>
struct Scan1<tuple<TS...>> {
static tuple<TS...> scan1(istream& in) {
return scan1_impl<0>(in);
}
private:
template<i64 I, SFINAE(sizeof...(TS) == I)>
static auto scan1_impl(istream&) {
return make_tuple();
}
template<i64 I, SFINAE(sizeof...(TS) > I)>
static auto scan1_impl(istream& in) {
using T = tuple_element_t<I,tuple<TS...>>;
auto head = make_tuple(Scan1<T>::scan1(in));
return tuple_cat(head, scan1_impl<I+1>(in));
}
};
template<typename T=i64>
T RD() {
return Scan<T>::scan(cin);
}
template<typename T=i64>
T RD1() {
return Scan1<T>::scan1(cin);
}
template<typename T=i64>
auto RD_VEC(i64 n) {
auto res = vec_reserve<T>(n);
REP(_, n) {
res.emplace_back(RD<T>());
}
return res;
}
template<typename T=i64>
auto RD1_VEC(i64 n) {
auto res = vec_reserve<T>(n);
REP(_, n) {
res.emplace_back(RD1<T>());
}
return res;
}
template<typename T=i64>
auto RD_VEC2(i64 h, i64 w) {
auto res = vec_reserve<vector<T>>(h);
REP(_, h) {
res.emplace_back(RD_VEC<T>(w));
}
return res;
}
template<typename T=i64>
auto RD1_VEC2(i64 h, i64 w) {
auto res = vec_reserve<vector<T>>(h);
REP(_, h) {
res.emplace_back(RD1_VEC<T>(w));
}
return res;
}
// }}}
// output {{{
template<typename T, typename Enable=void>
struct Fmt {
static void fmt(ostream& out, const T& x) { out << x; }
};
template<typename T>
void fmt_write(ostream& out, const T& x) {
Fmt<T>::fmt(out, x);
}
template<typename... TS>
struct Fmt<tuple<TS...>> {
static void fmt(ostream& out, const tuple<TS...>& t) {
tuple_enumerate(t, [&out](i64 i, const auto& e) {
if(i != 0) out << ' ';
fmt_write(out, e);
});
}
};
template<typename T1, typename T2>
struct Fmt<pair<T1,T2>> {
static void fmt(ostream& out, const pair<T1,T2>& p) {
return fmt_write(out, make_tuple(p.first,p.second));
}
};
template<typename C>
struct Fmt<C,enable_if_t<is_container<C>::value>> {
static void fmt(ostream& out, const C& c) {
for(auto it = begin(c); it != end(c); ++it) {
if(it != begin(c)) out << ' ';
fmt_write(out, *it);
}
}
};
void PRINT() {}
template<typename T, typename... TS>
void PRINT(const T& x, const TS&... args) {
fmt_write(cout, x);
if(sizeof...(args) > 0) {
cout << ' ';
PRINT(args...);
}
}
template<typename... TS>
void PRINTLN(const TS&... args) {
PRINT(args...);
cout << '\n';
}
// }}}
// debug {{{
template<typename T, typename Enable=void>
struct Dbg {
static void dbg(ostream& out, const T& x) { out << x; }
};
template<typename T>
void dbg_write(ostream& out, const T& x) {
return Dbg<T>::dbg(out, x);
}
template<>
struct Dbg<i64> {
static void dbg(ostream& out, i64 x) {
if(x == INF)
out << "INF";
else if(x == -INF)
out << "-INF";
else
out << x;
}
};
template<>
struct Dbg<f64> {
static void dbg(ostream& out, f64 x) {
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wfloat-equal"
if(x == FINF)
out << "FINF";
else if(x == -FINF)
out << "-FINF";
else
out << x;
#pragma GCC diagnostic pop
}
};
template<typename T, size_t N>
struct Dbg<T[N]> {
static void dbg(ostream& out, const T (&ary)[N]) {
out << "[";
REP(i, N) {
if(i != 0) out << ",";
dbg_write(out, ary[i]);
}
out << "]";
}
};
template<typename... TS>
struct Dbg<tuple<TS...>> {
static void dbg(ostream& out, const tuple<TS...>& t) {
out << "(";
tuple_enumerate(t, [&out](i64 i, const auto& e) {
if(i != 0) out << ",";
dbg_write(out, e);
});
out << ")";
}
};
template<typename T1, typename T2>
struct Dbg<pair<T1,T2>> {
static void dbg(ostream& out, const pair<T1,T2>& p) {
return dbg_write(out, make_tuple(p.first,p.second));
}
};
template<typename C>
struct Dbg<C,enable_if_t<is_container<C>::value>> {
static void dbg(ostream& out, const C& c) {
out << "[";
for(auto it = begin(c); it != end(c); ++it) {
if(it != begin(c)) out << ",";
dbg_write(out, *it);
}
out << "]";
}
};
template<typename T, typename C>
struct Dbg<stack<T,C>> {
static void dbg(ostream& out, stack<T,C> stk) {
out << "[";
while(!stk.empty()) {
dbg_write(out,stk.top()); stk.pop();
if(!stk.empty()) out << ",";
}
out << "]";
}
};
template<typename T, typename C>
struct Dbg<queue<T,C>> {
static void dbg(ostream& out, queue<T,C> que) {
out << "[";
while(!que.empty()) {
dbg_write(out,que.front()); que.pop();
if(!que.empty()) out << ",";
}
out << "]";
}
};
template<typename T, typename C, typename Comp>
struct Dbg<priority_queue<T,C,Comp>> {
static void dbg(ostream& out, priority_queue<T,C,Comp> que) {
out << "[";
while(!que.empty()) {
dbg_write(out,que.top()); que.pop();
if(!que.empty()) out << ",";
}
out << "]";
}
};
template<typename T>
void DBG_IMPL(i64 line, const char* expr, const T& value) {
cerr << "[L " << line << "]: ";
cerr << expr << " = ";
dbg_write(cerr, value);
cerr << "\n";
}
void DBG_IMPL_HELPER() {}
template<typename T, typename... TS>
void DBG_IMPL_HELPER(const T& x, const TS&... args) {
dbg_write(cerr, x);
if(sizeof...(args) > 0) {
cerr << ",";
DBG_IMPL_HELPER(args...);
}
}
template<typename... TS>
void DBG_IMPL(i64 line, const char* expr, const TS&... value) {
cerr << "[L " << line << "]: ";
cerr << "(" << expr << ") = (";
DBG_IMPL_HELPER(value...);
cerr << ")\n";
}
template<size_t N, typename T, SFINAE(rank<T>::value == 0)>
void DBG_DP_IMPL_HELPER(ostream& out, const T& x, const array<i64,N>&, const array<i64,N>&) {
dbg_write(out, x);
}
template<size_t N, typename T, SFINAE(rank<T>::value > 0)>
void DBG_DP_IMPL_HELPER(ostream& out, const T& x, const array<i64,N>& sizes, const array<i64,N>& offs) {
i64 k = N - rank<T>::value;
i64 off = offs[k];
i64 siz = sizes[k];
if(siz == 0) siz = extent<T>::value - off;
out << "[";
FOR(i, off, off+siz) {
if(i != off) out << ",";
DBG_DP_IMPL_HELPER(out, x[i], sizes, offs);
}
out << "]";
}
template<typename T, SFINAE(rank<T>::value > 0)>
void DBG_DP_IMPL(i64 line, const char* expr, const T& dp,
const array<i64,rank<T>::value>& sizes={},
const array<i64,rank<T>::value>& offs={})
{
cerr << "[L " << line << "]: ";
cerr << expr << " = ";
DBG_DP_IMPL_HELPER<rank<T>::value>(cerr, dp, sizes, offs);
cerr << "\n";
}
template<typename T>
void DBG_GRID_IMPL(i64 line, const char* expr, const vector<T>& grid) {
cerr << "[L " << line << "]: ";
cerr << expr << ":\n";
for(const auto& row : grid) {
dbg_write(cerr, row);
cerr << "\n";
}
cerr << "\n";
}
#ifdef PROCON_LOCAL
#define DBG(args...) DBG_IMPL(__LINE__, CPP_STR_I(args), args)
#define DBG_DP(args...) DBG_DP_IMPL(__LINE__, CPP_STR_I(args), args)
#define DBG_GRID(args...) DBG_GRID_IMPL(__LINE__, CPP_STR_I(args), args)
#else
#define DBG(args...)
#define DBG_DP(args...)
#define DBG_GRID(args...)
#endif
// }}}
// modint {{{
template<i64 M>
struct ModIntT {
static_assert(M >= 2, "");
i64 v_; // [0,M)
ModIntT() : v_(0) {}
ModIntT(i64 v) {
i64 r = v % M;
v_ = r >= 0 ? r : r+M;
}
ModIntT operator-() const {
return ModIntT(-v_);
}
ModIntT& operator+=(ModIntT rhs) {
v_ += rhs.v_;
v_ %= M;
return *this;
}
ModIntT& operator-=(ModIntT rhs) {
v_ += M;
v_ -= rhs.v_;
v_ %= M;
return *this;
}
ModIntT& operator*=(ModIntT rhs) {
v_ *= rhs.v_;
v_ %= M;
return *this;
}
ModIntT& operator++() {
return *this += 1;
}
ModIntT& operator--() {
return *this -= 1;
}
ModIntT operator++(int) {
return exchange(*this, *this+1);
}
ModIntT operator--(int) {
return exchange(*this, *this-1);
}
explicit operator i64() const { return v_; }
};
template<i64 M>
ModIntT<M> operator+(ModIntT<M> lhs, ModIntT<M> rhs) { return ModIntT<M>(lhs) += rhs; }
template<i64 M>
ModIntT<M> operator+(ModIntT<M> lhs, i64 rhs) { return ModIntT<M>(lhs) += rhs; }
template<i64 M>
ModIntT<M> operator+(i64 lhs, ModIntT<M> rhs) { return ModIntT<M>(rhs) += lhs; }
template<i64 M>
ModIntT<M> operator-(ModIntT<M> lhs, ModIntT<M> rhs) { return ModIntT<M>(lhs) -= rhs; }
template<i64 M>
ModIntT<M> operator-(ModIntT<M> lhs, i64 rhs) { return ModIntT<M>(lhs) -= rhs; }
template<i64 M>
ModIntT<M> operator-(i64 lhs, ModIntT<M> rhs) { return ModIntT<M>(rhs) -= lhs; }
template<i64 M>
ModIntT<M> operator*(ModIntT<M> lhs, ModIntT<M> rhs) { return ModIntT<M>(lhs) *= rhs; }
template<i64 M>
ModIntT<M> operator*(ModIntT<M> lhs, i64 rhs) { return ModIntT<M>(lhs) *= rhs; }
template<i64 M>
ModIntT<M> operator*(i64 lhs, ModIntT<M> rhs) { return ModIntT<M>(rhs) *= lhs; }
template<i64 M>
bool operator==(ModIntT<M> lhs, ModIntT<M> rhs) { return lhs.v_ == rhs.v_; }
template<i64 M>
bool operator==(ModIntT<M> lhs, i64 rhs) { return lhs == ModIntT<M>(rhs); }
template<i64 M>
bool operator==(i64 lhs, ModIntT<M> rhs) { return ModIntT<M>(lhs) == rhs; }
template<i64 M>
bool operator!=(ModIntT<M> lhs, ModIntT<M> rhs) { return !(lhs == rhs); }
template<i64 M>
bool operator!=(ModIntT<M> lhs, i64 rhs) { return !(lhs == rhs); }
template<i64 M>
bool operator!=(i64 lhs, ModIntT<M> rhs) { return !(lhs == rhs); }
template<i64 M>
struct Scan<ModIntT<M>> {
static ModIntT<M> scan(istream& in) {
return Scan<i64>::scan(in);
}
};
template<i64 M>
struct Fmt<ModIntT<M>> {
static void fmt(ostream& out, ModIntT<M> x) {
fmt_write(out, x.v_);
}
};
template<i64 M>
struct Dbg<ModIntT<M>> {
static void dbg(ostream& out, ModIntT<M> x) {
dbg_write(out, x.v_);
}
};
using ModInt = ModIntT<MOD>;
// }}}
// }}}
// init {{{
struct ProconInit {
static constexpr int IOS_PREC = 15;
static constexpr bool AUTOFLUSH = false;
ProconInit() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cin.exceptions(ios::failbit | ios::badbit);
cout << fixed << setprecision(IOS_PREC);
#ifdef PROCON_LOCAL
cerr << fixed << setprecision(IOS_PREC);
#endif
if(AUTOFLUSH)
cout << unitbuf;
}
} PROCON_INIT;
// }}}
//--------------------------------------------------------------------
void solve() {
i64 N = RD();
i64 P = RD();
auto A = RD_VEC2(N,3);
// コンテストi回目まででj問解いたときの順位の和の最小値
auto dp = vec_make<i64>(N+1,P+1, INF);
dp[0][0] = 0;
FOR(i, 1, N+1) REP(j, P+1) {
if(j > 3*i) continue;
const auto& row = A[i-1];
chmin(dp[i][j], dp[i-1][j] + row[0]);
if(j-1 >= 0) chmin(dp[i][j], dp[i-1][j-1] + row[1]);
if(j-2 >= 0) chmin(dp[i][j], dp[i-1][j-2] + row[2]);
if(j-3 >= 0) chmin(dp[i][j], dp[i-1][j-3] + 1);
}
f64 ans = f64(dp[N][P]) / f64(N);
PRINTLN(ans);
}
signed main() {
solve();
return 0;
}