結果
| 問題 | No.980 Fibonacci Convolution Hard |
| ユーザー |
 jell
|
| 提出日時 | 2020-02-01 01:42:41 |
| 言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 18,799 bytes |
| コンパイル時間 | 1,863 ms |
| コンパイル使用メモリ | 142,332 KB |
| 実行使用メモリ | 16,952 KB |
| 最終ジャッジ日時 | 2024-09-17 16:06:41 |
| 合計ジャッジ時間 | 8,998 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
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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 | TLE | - |
| testcase_01 | -- | - |
| testcase_02 | -- | - |
| testcase_03 | -- | - |
| testcase_04 | -- | - |
| testcase_05 | -- | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
ソースコード
/* preprocessor start */
#ifdef LOCAL
//*
#define _GLIBCXX_DEBUG // gcc
/*/
#define _LIBCPP_DEBUG 0 // clang
//*/
#define __clock__
// #define __buffer_check__
#else
#pragma GCC optimize("Ofast")
/*
#define _GLIBCXX_DEBUG // gcc
/*/
// #define _LIBCPP_DEBUG 0 // clang
//*/
// #define __buffer_check__
// #define NDEBUG
#endif
#define __precision__ 10
#define iostream_untie true
#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <complex>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <valarray>
#define __all(v) std::begin(v), std::end(v)
#define __rall(v) std::rbegin(v), std::rend(v)
#define __popcount(n) __builtin_popcountll(n)
#define __clz32(n) __builtin_clz(n)
#define __clz64(n) __builtin_clzll(n)
#define __ctz32(n) __builtin_ctz(n)
#define __ctz64(n) __builtin_ctzll(n)
/* preprocessor end */
namespace std
{
// hash
template <class T> size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash<T>()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); }
template <class T, class U> struct hash<pair<T, U>> { size_t operator()(pair<T, U> const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } };
template <class tuple_t, size_t index = tuple_size<tuple_t>::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc<tuple_t, index - 1>::apply(seed, t), get<index>(t)); } };
template <class tuple_t> struct tuple_hash_calc<tuple_t, 0> { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } };
template <class... T> struct hash<tuple<T...>> { size_t operator()(tuple<T...> const &t) const { return tuple_hash_calc<tuple<T...>>::apply(0, t); } };
// iostream
template <class T, class U> istream &operator>>(istream &is, pair<T, U> &p) { return is >> p.first >> p.second; }
template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { return os << p.first << ' ' << p.second; }
template <class tuple_t, size_t index> struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis<tuple_t, index - 1>::apply(is, t); return is >> get<index>(t); } };
template <class tuple_t> struct tupleis<tuple_t, SIZE_MAX> { static istream &apply(istream &is, tuple_t &t) { return is; } };
template <class... T> istream &operator>>(istream &is, tuple<T...> &t) { return tupleis<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(is, t); }
template <> istream &operator>>(istream &is, tuple<> &t) { return is; }
template <class tuple_t, size_t index> struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos<tuple_t, index - 1>::apply(os, t); return os << ' ' << get<index>(t); } };
template <class tuple_t> struct tupleos<tuple_t, 0> { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } };
template <class... T> ostream &operator<<(ostream &os, const tuple<T...> &t) { return tupleos<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(os, t); }
template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; }
template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; }
template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; }
} // namespace std
namespace setting
{
using namespace std;
using namespace chrono;
system_clock::time_point start_time, end_time;
long long get_elapsed_time() { end_time = system_clock::now(); return duration_cast<milliseconds>(end_time - start_time).count(); }
void print_elapsed_time() { cerr << "\n----- Exec time : " << get_elapsed_time() << " ms -----\n"; }
void buffer_check() { char bufc; if(cin >> bufc) cerr << "\n\033[1;35mwarning\033[0m: buffer not empty.\n"; }
struct setupper
{
setupper()
{
if(iostream_untie) ios::sync_with_stdio(false), cin.tie(nullptr);
cout << fixed << setprecision(__precision__);
#ifdef stderr_path
if(freopen(stderr_path, "a", stderr)) cerr << fixed << setprecision(__precision__);
#endif
#ifdef LOCAL
cerr << "\n----- stderr at LOCAL -----\n\n";
#endif
#ifdef __buffer_check__
atexit(buffer_check);
#endif
#ifdef __clock__
start_time = system_clock::now();
atexit(print_elapsed_time);
#endif
}
} __setupper; // struct setupper
} // namespace setting
#ifdef __clock__
#include "C:\Users\euler\OneDrive\Documents\Competitive_Programming\Library\local\Clock.hpp"
#else
#define build_clock() ((void)0)
#define set_clock() ((void)0)
#define get_clock() ((void)0)
#endif
#ifdef LOCAL
#include "C:\Users\euler\OneDrive\Documents\Competitive_Programming\Library\local\Dump.hpp"
#else
#define dump(...) ((void)0)
#endif
/* function utility start */
template <class T, class... types> T read(types... args) noexcept { typename std::remove_const<T>::type obj(args...); std::cin >> obj; return obj; }
#define input(type, var, ...) type var{read<type>(__VA_ARGS__)}
// substitute y for x if x > y.
template <class T> inline bool sbmin(T &x, const T &y) { return x > y ? x = y, true : false; }
// substitute y for x if x < y.
template <class T> inline bool sbmax(T &x, const T &y) { return x < y ? x = y, true : false; }
// binary search on discrete range.
template <class iter_type, class pred_type>
iter_type binary(iter_type __ok, iter_type __ng, pred_type pred)
{
std::ptrdiff_t dist(__ng - __ok);
while(std::abs(dist) > 1)
{
iter_type mid(__ok + dist / 2);
if(pred(mid)) __ok = mid, dist -= dist / 2;
else __ng = mid, dist /= 2;
}
return __ok;
}
// binary search on real numbers.
template <class pred_type>
long double binary(long double __ok, long double __ng, const long double eps, pred_type pred)
{
while(std::abs(__ok - __ng) > eps)
{
long double mid{(__ok + __ng) / 2};
(pred(mid) ? __ok : __ng) = mid;
}
return __ok;
}
// reset all bits.
template <class A> void reset(A &array) { memset(array, 0, sizeof(array)); }
// be careful that val is type-sensitive.
template <class T, class A, size_t N> void init(A (&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); }
/* functon utility end */
/* using alias start */
using namespace std;
using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t;
using pii = pair<i32, i32>; using pll = pair<i64, i64>;
template <class T, class Comp = less<T>> using heap = priority_queue<T, vector<T>, Comp>;
template <class T> using hashset = unordered_set<T>;
template <class Key, class Value> using hashmap = unordered_map<Key, Value>;
/* using alias end */
/* library start */
#ifndef Modint_hpp
#define Modint_hpp
#include <cassert>
#include <iostream>
template <int mod>
class modint
{
int val;
public:
constexpr modint() noexcept : val{0} {}
constexpr modint(long long x) noexcept : val((x %= mod) < 0 ? mod + x : x) {}
constexpr long long value() const noexcept { return val; }
constexpr modint operator++(int) noexcept { modint t = *this; return ++val, t; }
constexpr modint operator--(int) noexcept { modint t = *this; return --val, t; }
constexpr modint &operator++() noexcept { return ++val, *this; }
constexpr modint &operator--() noexcept { return --val, *this; }
constexpr modint operator-() const noexcept { return modint(-val); }
constexpr modint &operator+=(const modint &other) noexcept { return (val += other.val) < mod ? 0 : val -= mod, *this; }
constexpr modint &operator-=(const modint &other) noexcept { return (val += mod - other.val) < mod ? 0 : val -= mod, *this; }
constexpr modint &operator*=(const modint &other) noexcept { return val = (long long)val * other.val % mod, *this; }
constexpr modint &operator/=(const modint &other) noexcept { return *this *= inverse(other); }
constexpr modint operator+(const modint &other) const noexcept { return modint(*this) += other; }
constexpr modint operator-(const modint &other) const noexcept { return modint(*this) -= other; }
constexpr modint operator*(const modint &other) const noexcept { return modint(*this) *= other; }
constexpr modint operator/(const modint &other) const noexcept { return modint(*this) /= other; }
constexpr bool operator==(const modint &other) const noexcept { return val == other.val; }
constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; }
constexpr bool operator!() const noexcept { return !val; }
friend constexpr modint operator+(long long x, modint y) noexcept { return modint(x) + y; }
friend constexpr modint operator-(long long x, modint y) noexcept { return modint(x) - y; }
friend constexpr modint operator*(long long x, modint y) noexcept { return modint(x) * y; }
friend constexpr modint operator/(long long x, modint y) noexcept { return modint(x) / y; }
static constexpr modint inverse(const modint &other) noexcept
{
assert(other != 0);
int a{mod}, b{other.val}, u{}, v{1}, t{};
while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v;
return {u};
}
static constexpr modint pow(modint other, long long e) noexcept
{
if(e < 0) e = e % (mod - 1) + mod - 1;
modint res{1};
while(e) { if(e & 1) res *= other; other *= other, e >>= 1; }
return res;
}
friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; }
friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other = {(is >> val, val)}; return is; }
}; // class modint
template <>
class modint<2>
{
bool val;
public:
constexpr modint(bool x = false) noexcept : val{x} {}
constexpr modint(int x) noexcept : val(x & 1) {}
constexpr modint(long long x) noexcept : val(x & 1) {}
constexpr operator bool() const noexcept { return val; }
constexpr bool value() const noexcept { return val; }
constexpr modint &operator+=(const modint &other) noexcept { return val ^= other.val, *this; }
constexpr modint &operator-=(const modint &other) noexcept { return val ^= other.val, *this; }
constexpr modint &operator*=(const modint &other) noexcept { return val &= other.val, *this; }
constexpr modint &operator/=(const modint &other) noexcept { assert(other.val); return *this; }
constexpr modint operator!() const noexcept { return !val; }
constexpr modint operator-() const noexcept { return *this; }
constexpr modint operator+(const modint &other) const noexcept { return val != other.val; }
constexpr modint operator-(const modint &other) const noexcept { return val != other.val; }
constexpr modint operator*(const modint &other) const noexcept { return val && other.val; }
constexpr modint operator/(const modint &other) const noexcept { assert(other.val); return *this; }
constexpr bool operator==(const modint &other) const noexcept { return val == other.val; }
constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; }
friend constexpr modint operator+(long long x, modint y) noexcept { return x & 1 ? !y : y; }
friend constexpr modint operator-(long long x, modint y) noexcept { return x & 1 ? !y : y; }
friend constexpr modint operator*(long long x, modint y) noexcept { return x & 1 ? y : modint<2>{0}; }
friend constexpr modint operator/(long long x, modint y) noexcept { assert(y.val); return x & 1 ? y : modint<2>{0}; }
friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; }
friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other.val = (is >> val, val & 1); return is; }
}; // class modint specialization
#endif // Modint_hpp
#ifndef Matrix_hpp
#define Matrix_hpp
#include <iostream>
#include <valarray>
#include <vector>
template <class Field>
class matrix
{
size_t h, w;
using row_type = std::valarray<Field>;
using data_type = std::valarray<std::valarray<Field>>;
data_type data;
friend std::istream &operator>>(std::istream &is, matrix &x)
{
for(size_t i = 0; i != x.h; ++i)
{
for(size_t j = 0; j != x.w; ++j) is >> x.data[i][j];
}
return is;
}
friend std::ostream &operator<<(std::ostream &os, const matrix &x)
{
for(size_t i = 0; i != x.h; ++i)
{
if(i) os << "\n";
for(size_t j = 0; j != x.w; ++j) os << (j ? " " : "") << x.data[i][j];
}
return os;
}
friend matrix transpose(const matrix &x)
{
matrix res(x.w, x.h);
for(size_t i = 0; i != x.w; ++i)
for(size_t j = 0; j != x.h; ++j)
res[i][j] = x.data[j][i];
return res;
}
friend matrix pow(matrix x, long long n)
{
assert(x.square());
if(n < 0) x = inverse(x), n = -n;
matrix res{identity(x.h)};
while(n)
{
if(n & 1) res *= x;
x *= x, n >>= 1;
}
return res;
}
friend matrix inverse(const matrix &x)
{
assert(x.square());
matrix ext_x(x.h, x.h * 2), res(x.h);
for(size_t i = 0; i != x.h; ++i) ext_x.data[i][std::slice(0, x.h, 1)] = x.data[i], ext_x.data[i][i + x.h] = 1;
if(ext_x.row_canonicalize().size() != x.h) return matrix{0};
for(size_t i = 0; i != x.h; ++i) res[i] = ext_x.data[i][std::slice(x.h, x.h, 1)];
return res;
}
public:
explicit matrix(size_t _n = 0) : h(_n), w(_n) { resize(_n, _n);}
matrix(size_t _h, size_t _w) : h(_h), w(_w) { resize(_h, _w); }
matrix(const data_type &_data) : h(_data.size()), w(_data.size() ? _data[0].size() : 0), data(_data) {}
operator data_type() const { return data; }
size_t height() const noexcept { return h; }
size_t width() const noexcept { return w; }
bool square() const noexcept { return h == w; }
row_type &operator[](const size_t i) noexcept { assert(i < data.size()); return data[i]; }
void resize(size_t h, size_t w, const Field val = Field(0)) { data.resize(h, std::valarray<Field>(val, w)); }
static matrix identity(const size_t n) noexcept
{
data_type data(row_type(n), n);
for(size_t i = 0; i != n; ++i) data[i][i] = 1;
return data;
}
matrix operator-() const noexcept { return {-data}; }
matrix &operator+=(const matrix &other) noexcept { data += other.data; return *this; }
matrix &operator-=(const matrix &other) { data -= other.data; return *this; }
matrix &operator*=(matrix other) noexcept
{
other = transpose(other);
for(size_t i = 0; i != h; ++i)
{
const row_type copied{data[i]};
for(size_t j = 0; j != other.h; ++j) data[i][j] = (copied * other.data[j]).sum();
}
return *this;
}
matrix operator+(const matrix &x) const noexcept { return matrix(*this) += x; }
matrix operator-(const matrix &x) const noexcept { return matrix(*this) -= x; }
matrix operator*(const matrix &x) const noexcept { return matrix(*this) *= x; }
// return the list of pivot columns
std::vector<size_t> row_canonicalize()
{
std::vector<size_t> pivots;
for(size_t j = 0, rank = 0; j != w; ++j)
{
row_type *row_ptr = nullptr;
for(size_t i = rank; i != h; ++i)
{
if(data[i][j] != Field{0})
{
const Field f = data[i][j];
if(row_ptr) data[i][std::slice(j, w - j, 1)] -= *row_ptr * f;
else
{
swap(data[rank], data[i]);
std::slice_array<Field> tmp{data[rank][std::slice(j, w - j, 1)]};
tmp = *(row_ptr = new row_type{tmp}) /= f;
}
}
}
if(row_ptr)
{
for(size_t k = 0; k != rank; ++k)
{
const Field f = data[k][j];
data[k][std::slice(j, w - j, 1)] -= *row_ptr * f;
}
++rank;
pivots.emplace_back(j);
delete row_ptr;
}
}
return pivots;
}
Field determinant() const
{
assert(square());
data_type copied{data};
Field res{1};
for(size_t j = 0; j != w; ++j)
{
row_type *row_ptr = nullptr;
for(size_t i = j; i != h; ++i)
{
if(copied[i][j] != Field{0})
{
const Field f = copied[i][j];
if(row_ptr) copied[i][std::slice(j, w - j, 1)] -= *row_ptr * f;
else
{
swap(copied[i], copied[j]);
if(i != j) res = -res;
res *= f;
std::slice_array<Field> tmp{copied[j][std::slice(j, w - j, 1)]};
tmp = *(row_ptr = new row_type{tmp}) /= f;
}
}
}
if(!row_ptr) return 0;
}
return res;
}
}; // class matrix
#endif // Matrix_hpp
/* library end */
/* The main code follows. */
using mint=modint<(int)1e9+7>;
struct solver
{
solver()
{
input(mint,p);
matrix<mint> t({
{p,1,0,0},
{1,0,0,0},
{0,1,p,1},
{0,0,1,0}
});
input(int,Q);
while(Q--)
{
int q; cin>>q;
q-=2;
cout << pow(t,q)[2][0] << "\n";
}
}
}; // struct solver
int main(int argc, char *argv[])
{
u32 t; // loop count
#ifdef LOCAL
t = 1;
#else
t = 1; // single test case
#endif
// t = -1; // infinite loop
// cin >> t; // case number given
while(t--)
{
solver();
}
}