結果
| 問題 |
No.2883 K-powered Sum of Fibonacci
|
| ユーザー |
 t98slider
|
| 提出日時 | 2024-09-08 14:02:08 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 241 ms / 3,000 ms |
| コード長 | 6,173 bytes |
| コンパイル時間 | 2,283 ms |
| コンパイル使用メモリ | 200,488 KB |
| 最終ジャッジ日時 | 2025-02-24 05:37:17 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 40 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template<const unsigned int MOD> struct prime_modint {
using mint = prime_modint;
unsigned int v;
prime_modint() : v(0) {}
prime_modint(unsigned int a) { a %= MOD; v = a; }
prime_modint(unsigned long long a) { a %= MOD; v = a; }
prime_modint(int a) { a %= (int)(MOD); if(a < 0)a += MOD; v = a; }
prime_modint(long long a) { a %= (int)(MOD); if(a < 0)a += MOD; v = a; }
static constexpr int mod() { return MOD; }
mint& operator++() {v++; if(v == MOD)v = 0; return *this;}
mint& operator--() {if(v == 0)v = MOD; 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 >= MOD) v -= MOD; return *this; }
mint& operator-=(const mint& rhs) { if(v < rhs.v) v += MOD; v -= rhs.v; return *this; }
mint& operator*=(const mint& rhs) {
v = (unsigned int)((unsigned long long)(v) * rhs.v % MOD);
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 r = 1, x = *this;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const { assert(v); return pow(MOD - 2); }
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); }
friend std::ostream& operator << (std::ostream &os, const mint& rhs) noexcept { return os << rhs.v; }
};
//using mint = prime_modint<1000000007>;
using mint = prime_modint<998244353>;
//enumeration<mint> enu(200000);のように宣言する
template<class T> struct enumeration{
int N;
vector<T> fact, inv;
enumeration() : N(0), fact(1, 1), inv(1, 1) {}
enumeration(int _n) : N(_n), fact(_n + 1), inv(_n + 1) {
fact[0] = 1;
for(int i = 1; i <= N; i++) fact[i] = fact[i - 1] * i;
inv[N] = T(1) / fact[N];
for(int i = N; i >= 1; i--) inv[i - 1] = inv[i] * i;
}
void expand(int lim){
fact.resize(lim + 1);
inv.resize(lim + 1);
for(int i = N + 1; i <= lim; i++) fact[i] = i * fact[i - 1];
inv[lim] = T(1) / fact[lim];
for(int i = lim; i >= N + 2; i--) inv[i - 1] = i * inv[i];
N = lim;
}
T Per(int n, int k){
if(k > n) return 0;
if(n > N) expand(n);
return fact[n] * inv[n - k];
}
T C(int n, int k){
if(n < 0 || k < 0 || k > n) return 0;
if(n > N) expand(n);
return fact[n] * inv[n - k] * inv[k];
}
T H(int n, int k){
if(n ==0 && k == 0) return 1;
if(n <= 0 || k < 0) return 0;
return C(n + k - 1, k);
}
};
template <class T, size_t N> struct Matrix {
std::array<std::array<T, N>, N> A{};
Matrix() {}
Matrix(const std::array<std::array<T, N>, N> &M) : A(M){}
Matrix(const std::vector<std::vector<T>> &M) {
for(size_t i = 0; i < N; i++){
for(size_t j = 0; j < N; j++){
A[i][j] = M[i][j];
}
}
}
const std::array<T, N>& operator[](int i) const { return A[i]; }
std::array<T, N>& operator[](int i) { return A[i]; }
Matrix& operator+=(const Matrix& rhs) {
for(size_t i = 0; i < N; i++){
for(size_t j = 0; j < N; j++){
A[i][j] += rhs[i][j];
}
}
return *this;
}
Matrix& operator-=(const Matrix& rhs) {
for(size_t i = 0; i < N; i++){
for(size_t j = 0; j < N; j++){
A[i][j] -= rhs[i][j];
}
}
return *this;
}
Matrix& operator*=(const Matrix& rhs) {
std::array<std::array<T, N>, N> res{};
for(size_t i = 0; i < N; i++){
for(size_t j = 0; j < N; j++){
for(size_t k = 0; k < N; k++){
res[i][j] += A[i][k] * rhs[k][j];
}
}
}
swap(A, res);
return *this;
}
Matrix& operator+() const { return *this; }
Matrix& operator-() const { return Matrix() - *this; }
friend Matrix operator+(const Matrix& lhs, const Matrix& rhs) {
return Matrix(lhs) += rhs;
}
friend Matrix operator-(const Matrix& lhs, const Matrix& rhs) {
return Matrix(lhs) -= rhs;
}
friend Matrix operator*(const Matrix& lhs, const Matrix& rhs) {
return Matrix(lhs) *= rhs;
}
friend bool operator==(const Matrix& lhs, const Matrix& rhs) {
return (lhs.A == rhs.A);
}
friend bool operator!=(const Matrix& lhs, const Matrix& rhs) {
return (lhs.A != rhs.A);
}
Matrix pow(long long v){
Matrix res, temp = A;
for(size_t i = 0; i < N; i++)res[i][i] = 1;
while(v){
if(v & 1)res *= temp;
temp *= temp;
v >>= 1;
}
return res;
}
friend std::ostream& operator << (std::ostream &os, const Matrix& rhs) noexcept {
for(size_t i = 0; i < N; i++){
if(i) os << '\n';
for(size_t j = 0; j < N; j++){
os << (j ? " " : "") << rhs[i][j];
}
}
return os;
}
};
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
ll n, k;
cin >> n >> k;
Matrix<mint, 102> Mt;
enumeration<mint> enu(1000);
for(int i = 0; i <= k; i++){
// F2**(i) * F1**(k-i) を求める
for(int j = 0; j <= i; j++){
// F1**(j) * F0**(i-j) からの寄与
Mt[j + k - i][i] += enu.C(i, j);
}
}
Mt[k][101] = Mt[101][101] = 1;
auto B = Mt.pow(n);
// cout << B << '\n';
mint ans = B[k][101];
cout << ans << '\n';
}