結果
| 問題 | No.3457 Fibo-shrink |
| コンテスト | |
| ユーザー |
 tomolatoon
|
| 提出日時 | 2026-02-28 14:20:06 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 21,908 bytes |
| 記録 | |
| コンパイル時間 | 6,081 ms |
| コンパイル使用メモリ | 285,756 KB |
| 実行使用メモリ | 7,844 KB |
| 最終ジャッジ日時 | 2026-02-28 14:20:13 |
| 合計ジャッジ時間 | 7,080 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 11 RE * 1 |
ソースコード
//#include <bits/stdc++.h>
#include <algorithm>
#include <bit>
#include <cassert>
#include <charconv>
#include <cmath>
#include <cstdint>
#include <deque>
#include <functional>
#include <initializer_list>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <ranges>
#include <set>
#include <span>
#include <stack>
#include <string>
#include <string_view>
#include <tuple>
#include <vector>
#ifndef ATCODER_MODINT_HPP
# define ATCODER_MODINT_HPP 1
# include <cassert>
# include <numeric>
# include <type_traits>
# ifdef _MSC_VER
# include <intrin.h>
# endif
# ifndef ATCODER_INTERNAL_MATH_HPP
# define ATCODER_INTERNAL_MATH_HPP 1
# include <utility>
# ifdef _MSC_VER
# include <intrin.h>
# endif
namespace atcoder
{
namespace internal
{
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m)
{
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett
{
unsigned int _m;
unsigned long long im;
// @param m `1 <= m`
explicit barrett(unsigned int m)
: _m(m), im((unsigned long long)(-1) / m + 1)
{}
// @return m
unsigned int umod() const
{
return _m;
}
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const
{
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
# ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
# else
unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
# endif
unsigned long long y = x * _m;
return (unsigned int)(z - y + (z < y ? _m : 0));
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m)
{
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n)
{
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n)
{
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0)
d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases)
{
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1)
{
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0)
{
return false;
}
}
return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b)
{
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t)
{
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m)
{
if (m == 2) return 1;
if (m == 167'772161) return 3;
if (m == 469'762049) return 3;
if (m == 754'974721) return 11;
if (m == 998'244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0)
x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2)
{
if (x % i == 0)
{
divs[cnt++] = i;
while (x % i == 0)
{
x /= i;
}
}
}
if (x > 1)
{
divs[cnt++] = x;
}
for (int g = 2;; g++)
{
bool ok = true;
for (int i = 0; i < cnt; i++)
{
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1)
{
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long
floor_sum_unsigned(unsigned long long n, unsigned long long m, unsigned long long a, unsigned long long b)
{
unsigned long long ans = 0;
while (true)
{
if (a >= m)
{
ans += n * (n - 1) / 2 * (a / m);
a %= m;
}
if (b >= m)
{
ans += n * (b / m);
b %= m;
}
unsigned long long y_max = a * n + b;
if (y_max < m) break;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
# endif // ATCODER_INTERNAL_MATH_HPP
# ifndef ATCODER_INTERNAL_TYPE_TRAITS_HPP
# define ATCODER_INTERNAL_TYPE_TRAITS_HPP 1
# include <cassert>
# include <numeric>
# include <type_traits>
namespace atcoder
{
namespace internal
{
# ifndef _MSC_VER
template <class T>
using is_signed_int128 = typename std::conditional<
std::is_same<T, __int128_t>::value || std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 = typename std::conditional<
std::is_same<T, __uint128_t>::value || std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<
std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<
(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int = typename std::conditional<
(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>, std::common_type<T>>::type>::type;
# else
template <class T>
using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int = typename std::
conditional<is_integral<T>::value && std::is_signed<T>::value, std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int = typename std::
conditional<is_integral<T>::value && std::is_unsigned<T>::value, std::true_type, std::false_type>::type;
template <class T>
using to_unsigned =
typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>, std::common_type<T>>::type;
# endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
# endif // ATCODER_INTERNAL_TYPE_TRAITS_HPP
namespace atcoder
{
namespace internal
{
struct modint_base
{};
struct static_modint_base: modint_base
{};
template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint: internal::static_modint_base
{
using mint = static_modint;
public:
static constexpr int mod()
{
return m;
}
static mint raw(int v)
{
mint x;
x._v = v;
return x;
}
static_modint()
: _v(0)
{}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v)
{
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v)
{
_v = (unsigned int)(v % umod());
}
unsigned int val() const
{
return _v;
}
mint& operator++()
{
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--()
{
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int)
{
mint result = *this;
++*this;
return result;
}
mint operator--(int)
{
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs)
{
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs)
{
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs)
{
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs)
{
return *this = *this * rhs.inv();
}
mint operator+() const
{
return *this;
}
mint operator-() const
{
return mint() - *this;
}
mint pow(long long n) const
{
assert(0 <= n);
mint x = *this, r = 1;
while (n)
{
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const
{
if (prime)
{
assert(_v);
return pow(umod() - 2);
}
else
{
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs)
{
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs)
{
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs)
{
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs)
{
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs)
{
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs)
{
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod()
{
return m;
}
static constexpr bool prime = internal::is_prime<m>;
};
template <int id>
struct dynamic_modint: internal::modint_base
{
using mint = dynamic_modint;
public:
static int mod()
{
return (int)(bt.umod());
}
static void set_mod(int m)
{
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v)
{
mint x;
x._v = v;
return x;
}
dynamic_modint()
: _v(0)
{}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v)
{
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v)
{
_v = (unsigned int)(v % mod());
}
unsigned int val() const
{
return _v;
}
mint& operator++()
{
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--()
{
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int)
{
mint result = *this;
++*this;
return result;
}
mint operator--(int)
{
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs)
{
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs)
{
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs)
{
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs)
{
return *this = *this * rhs.inv();
}
mint operator+() const
{
return *this;
}
mint operator-() const
{
return mint() - *this;
}
mint pow(long long n) const
{
assert(0 <= n);
mint x = *this, r = 1;
while (n)
{
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const
{
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs)
{
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs)
{
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs)
{
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs)
{
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs)
{
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs)
{
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod()
{
return bt.umod();
}
};
template <int id>
internal::barrett dynamic_modint<id>::bt(998'244353);
using modint998244353 = static_modint<998'244353>;
using modint1000000007 = static_modint<1000'000007>;
using modint = dynamic_modint<-1>;
namespace internal
{
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class>
struct is_dynamic_modint: public std::false_type
{};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>>: public std::true_type
{};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#endif // ATCODER_MODINT_HPP
// #define OLD_JUDGE
#ifdef OLD_JUDGE
# define USE_ISTREAM
# define USE_OSTREAM
#else
# define USE_ISTREAM
# define USE_PRINT
#endif
#if defined(USE_ISTREAM) || defined(USE_OSTREAM)
# include <iomanip>
# include <iostream>
#endif
#ifdef USE_PRINT
# include <format>
# include <print>
#endif
namespace tomolatoon
{
using namespace std::views;
namespace rng = std::ranges;
#ifdef USE_ISTREAM
using std::cin;
#endif
#ifdef USE_OSTREAM
using std::cout;
using std::endl;
#endif
#ifdef USE_PRINT
using std::format;
using std::print;
using std::println;
template <class T>
void pr(T&& t)
{
print("{}", std::forward<T>(t));
}
template <class T>
void prn(T&& t)
{
println("{}", std::forward<T>(t));
}
#endif
using rng::subrange;
using std::array;
using std::deque;
using std::list;
using std::map;
using std::multimap;
using std::multiset;
using std::pair;
using std::queue;
using std::set;
using std::span;
using std::stack;
using std::string;
using std::string_view;
using std::tuple;
using std::vector;
template <class T>
using vec = vector<T>;
using uint = std::uint32_t;
using ull = std::uint64_t;
using ll = std::int64_t;
using std::size_t;
// clang-format off
using rng::all_of;
using rng::any_of;
#ifndef OLD_JUDGE
using rng::none_of;
using rng::contains;
using rng::contains_subrange;
#endif
using rng::for_each;
using rng::for_each_n;
using rng::find;
using rng::find_if;
using rng::find_if_not;
#ifndef OLD_JUDGE
using rng::find_last;
using rng::find_last_if;
using rng::find_last_if_not;
#endif
using rng::find_end;
using rng::find_first_of;
using rng::adjacent_find;
using rng::count;
using rng::count_if;
using rng::mismatch;
using rng::equal;
using rng::search;
using rng::search_n;
// clang-format on
using rng::sort;
using rng::stable_sort;
using rng::unique;
using rng::max_element;
using rng::min_element;
using rng::binary_search;
using rng::equal_range;
using rng::lower_bound;
using rng::upper_bound;
using rng::next_permutation;
using rng::prev_permutation;
using rng::begin;
using rng::distance;
using rng::end;
using rng::ssize;
using rng::swap;
using std::abs;
using std::midpoint;
using std::back_inserter;
using std::front_inserter;
using std::inserter;
using namespace std::placeholders;
void yn(bool f)
{
#ifdef USE_OSTREAM
cout << (f ? "Yes" : "No") << "\n";
#elifdef USE_PRINT
println("{}", (f ? "Yes" : "No"));
#endif
}
string yns(bool f)
{
return f ? "Yes" : "No";
}
// clang-format off
struct P
{
using type = ll;
type i;
type j;
P moved(type id, type jd) const { return {i + id, j + jd}; }
P moved(P pd) const { return moved(pd.i, pd.j); }
template <class T>
T& operator[](vec<vec<T>>& v) const { return v[i][j]; }
char& operator[](vec<string>& v) const { return v[i][j]; }
friend P operator+(const P& lhs, const P& rhs) { return lhs.moved(rhs); }
friend P operator-(const P& lhs, const P& rhs) { return lhs.moved(-rhs); }
P operator-() const { return P{-i, -j}; }
friend bool operator==(const P& lhs, const P& rhs) { return lhs.i == rhs.i && lhs.j == rhs.j; }
friend auto operator<=>(const P& lhs, const P& rhs) { return lhs.i != rhs.i ? lhs.i <=> rhs.i : lhs.j <=> rhs.j; }
ll L1() const { return std::abs(i) + std::abs(j); }
friend ll ip(const P& lhs, const P& rhs) { return lhs.i * rhs.i + lhs.j * rhs.j; }
};
const auto in_f = [](P::type h, P::type w) { return [=](P p) { return 0 <= p.i && p.i < h && 0 <= p.j && p.j < w; }; };
static const auto P4 = array<P, 4>{P{-1, 0}, P{ 0, -1}, P{ 1, 0}, P{ 0, 1}};
static const auto P8 = array<P, 8>{P{-1, 0}, P{-1, -1}, P{ 0, -1}, P{ 1, -1}, P{ 1, 0}, P{ 1, 1}, P{ 0, 1}, P{-1, 1}};
// clang-format on
ll pow(ll base, size_t n)
{
assert(not(base == 0 && n == 0));
if (n == 0) return 1;
if (n == 1) return base;
ll prev = pow(base, n / 2);
return prev * prev * (n % 2 ? base : 1);
}
ll pow(ll base, size_t n, ll mod)
{
assert(not(base == 0 && n == 0));
constexpr auto modf = [](ll x, ll mod) {
return (x % mod + mod) % mod;
};
if (base >= mod) base %= mod;
if (n == 0) return 1;
if (n == 1) return base;
ll prev = pow(base, n / 2);
ll pp = modf(prev * prev, mod);
return (n % 2 ? modf(pp * base, mod) : pp);
}
template <class T>
T shared_length_signed(T l1, T r1, T l2, T r2)
{
return rng::min(r1, r2) - rng::max(l1, l2);
}
template <class T>
T shared_length(T l1, T r1, T l2, T r2)
{
return rng::max(0, rng::min(r1, r2) - rng::max(l1, l2));
}
/// @brief ランレングス圧縮（RLE: Run Length Encoding）を行い，出力イテレータへ書き込む
/// @note vec<pair<T, size_t>>をreserveし，それのback_inserter(back_insert_iterator)を渡すことが想定される
/// @param r ランレングス圧縮したいrange
/// @param out 出力イテレータ
template <rng::forward_range R, std::output_iterator<std::pair<rng::range_value_t<R>, size_t>> I>
requires std::copyable<rng::range_value_t<R>> && std::equality_comparable<rng::range_value_t<R>>
void rle(R&& r, I out)
{
using pair = std::pair<rng::range_value_t<R>, size_t>;
auto it = begin(r);
auto e = end(r);
if (it == e)
{
return;
}
size_t size = 1;
rng::range_value_t<R> prev = *it;
++it;
for (; it != e; ++it)
{
if (*it == prev)
{
++size;
}
else
{
*out++ = pair(std::move(prev), size);
prev = *it;
size = 1;
}
}
*out++ = pair(std::move(prev), size);
}
namespace detail
{
template <size_t N>
struct get
{
template <class T>
// static
constexpr decltype(auto) operator()(T&& t) noexcept(noexcept(std::get<N>(t)))
{
return std::get<N>(t);
}
};
} // namespace detail
template <size_t N>
inline constexpr auto get = detail::get<N>{};
constexpr ll INF = 3e18;
} // namespace tomolatoon
namespace tomolatoon
{
using namespace atcoder;
using mint = static_modint<10007>;
void solve()
{
ll k, s, n;
cin >> k >> s >> n;
vec<mint> fib(rng::max(k, n) + 100);
fib[0] = 1;
fib[1] = 1;
for (auto i : iota(2, ssize(fib)))
{
fib[i] = fib[i - 1] + fib[i - 2];
}
vec<mint> fib_inv(ssize(fib));
for (auto i : iota(0, ssize(fib)))
{
fib_inv[i] = fib[i].inv();
}
vec<mint> sfib(n);
sfib[0] = s;
for (auto i : iota(0, n - 1))
{
for (auto j : iota(0, k + 1))
{
if (i - j >= 0)
{
sfib[i + 1] += sfib[i - j] * fib_inv[j];
}
}
}
prn(sfib.back().val());
}
} // namespace tomolatoon
int main()
{
#ifdef USE_ISTREAM
std::cin.tie(nullptr);
std::ios::sync_with_stdio(false);
#endif
#ifdef USE_OSTREAM
std::cout << std::fixed << std::setprecision(16);
#endif
tomolatoon::solve();
#ifdef USE_OSTREAM
std::cout << std::flush;
#endif
}