結果
問題 | No.2883 K-powered Sum of Fibonacci |
ユーザー | 👑 binap |
提出日時 | 2024-09-22 20:46:44 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 4 ms / 3,000 ms |
コード長 | 17,041 bytes |
コンパイル時間 | 5,423 ms |
コンパイル使用メモリ | 288,352 KB |
実行使用メモリ | 6,944 KB |
最終ジャッジ日時 | 2024-09-22 20:46:51 |
合計ジャッジ時間 | 6,697 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge5 |
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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 | AC | 2 ms
6,816 KB |
testcase_01 | AC | 2 ms
6,940 KB |
testcase_02 | AC | 2 ms
6,940 KB |
testcase_03 | AC | 2 ms
6,944 KB |
testcase_04 | AC | 2 ms
6,940 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 | 2 ms
6,944 KB |
testcase_09 | AC | 2 ms
6,944 KB |
testcase_10 | AC | 2 ms
6,944 KB |
testcase_11 | AC | 3 ms
6,944 KB |
testcase_12 | AC | 3 ms
6,940 KB |
testcase_13 | AC | 2 ms
6,940 KB |
testcase_14 | AC | 3 ms
6,940 KB |
testcase_15 | AC | 3 ms
6,944 KB |
testcase_16 | AC | 2 ms
6,944 KB |
testcase_17 | AC | 2 ms
6,944 KB |
testcase_18 | AC | 2 ms
6,940 KB |
testcase_19 | AC | 2 ms
6,940 KB |
testcase_20 | AC | 3 ms
6,944 KB |
testcase_21 | AC | 4 ms
6,940 KB |
testcase_22 | AC | 3 ms
6,944 KB |
testcase_23 | AC | 4 ms
6,944 KB |
testcase_24 | AC | 3 ms
6,940 KB |
testcase_25 | AC | 4 ms
6,940 KB |
testcase_26 | AC | 3 ms
6,944 KB |
testcase_27 | AC | 4 ms
6,940 KB |
testcase_28 | AC | 3 ms
6,940 KB |
testcase_29 | AC | 3 ms
6,940 KB |
testcase_30 | AC | 2 ms
6,940 KB |
testcase_31 | AC | 2 ms
6,944 KB |
testcase_32 | AC | 2 ms
6,940 KB |
testcase_33 | AC | 2 ms
6,940 KB |
testcase_34 | AC | 2 ms
6,940 KB |
testcase_35 | AC | 2 ms
6,940 KB |
testcase_36 | AC | 2 ms
6,940 KB |
testcase_37 | AC | 2 ms
6,940 KB |
testcase_38 | AC | 2 ms
6,944 KB |
testcase_39 | AC | 2 ms
6,940 KB |
testcase_40 | AC | 2 ms
6,940 KB |
testcase_41 | AC | 2 ms
6,940 KB |
testcase_42 | AC | 3 ms
6,940 KB |
ソースコード
#include<bits/stdc++.h> #include<atcoder/all> #define rep(i,n) for(int i=0;i<n;i++) using namespace std; using namespace atcoder; typedef long long ll; typedef vector<int> vi; typedef vector<long long> vl; typedef vector<vector<int>> vvi; typedef vector<vector<long long>> vvl; typedef long double ld; typedef pair<int, int> P; template <int m> ostream& operator<<(ostream& os, const static_modint<m>& a) {os << a.val(); return os;} template <int m> ostream& operator<<(ostream& os, const dynamic_modint<m>& a) {os << a.val(); return os;} template <int m> istream& operator>>(istream& is, static_modint<m>& a) {long long x; is >> x; a = x; return is;} template <int m> istream& operator>>(istream& is, dynamic_modint<m>& a) {long long x; is >> x; a = x; return is;} template<typename T> istream& operator>>(istream& is, vector<T>& v){int n = v.size(); assert(n > 0); rep(i, n) is >> v[i]; return is;} template<typename U, typename T> ostream& operator<<(ostream& os, const pair<U, T>& p){os << p.first << ' ' << p.second; return os;} template<typename T> ostream& operator<<(ostream& os, const vector<T>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : " "); return os;} template<typename T> ostream& operator<<(ostream& os, const vector<vector<T>>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : ""); return os;} template<typename T> ostream& operator<<(ostream& os, const set<T>& se){for(T x : se) os << x << " "; os << "\n"; return os;} template<typename T> ostream& operator<<(ostream& os, const unordered_set<T>& se){for(T x : se) os << x << " "; os << "\n"; return os;} template<typename S, auto op, auto e> ostream& operator<<(ostream& os, const atcoder::segtree<S, op, e>& seg){int n = seg.max_right(0, [](S){return true;}); rep(i, n) os << seg.get(i) << (i == n - 1 ? "\n" : " "); return os;} template<typename S, auto op, auto e, typename F, auto mapping, auto composition, auto id> ostream& operator<<(ostream& os, const atcoder::lazy_segtree<S, op, e, F, mapping, composition, id>& seg){int n = seg.max_right(0, [](S){return true;}); rep(i, n) os << seg.get(i) << (i == n - 1 ? "\n" : " "); return os;} template<typename T> void chmin(T& a, T b){a = min(a, b);} template<typename T> void chmax(T& a, T b){a = max(a, b);} using mint = modint998244353; // combination mod prime // https://youtu.be/8uowVvQ_-Mo?t=6002 // https://youtu.be/Tgd_zLfRZOQ?t=9928 struct modinv { int n; vector<mint> d; modinv(): n(2), d({0,1}) {} mint operator()(int i) { while (n <= i) d.push_back(-d[mint::mod()%n]*(mint::mod()/n)), ++n; return d[i]; } mint operator[](int i) const { return d[i];} } invs; struct modfact { int n; vector<mint> d; modfact(): n(2), d({1,1}) {} mint operator()(int i) { while (n <= i) d.push_back(d.back()*n), ++n; return d[i]; } mint operator[](int i) const { return d[i];} } facts; struct modfactinv { int n; vector<mint> d; modfactinv(): n(2), d({1,1}) {} mint operator()(int i) { while (n <= i) d.push_back(d.back()*invs(n)), ++n; return d[i]; } mint operator[](int i) const { return d[i];} } ifacts; mint comb(int n, int k) { if (n < k || k < 0) return 0; return facts(n)*ifacts(k)*ifacts(n-k); } template< typename T > struct FormalPowerSeries : vector< T > { using vector< T >::vector; using P = FormalPowerSeries; template<class...Args> FormalPowerSeries(Args...args): vector<T>(args...) {} FormalPowerSeries(initializer_list<T> a): vector<T>(a.begin(),a.end()) {} using MULT = function< P(P, P) >; static MULT &get_mult() { static MULT mult = [&](P a, P b){ P res(convolution(a, b)); return res; }; return mult; } static void set_fft(MULT f) { get_mult() = f; } void shrink() { while(this->size() && this->back() == T(0)) this->pop_back(); } P operator+(const P &r) const { return P(*this) += r; } P operator+(const T &v) const { return P(*this) += v; } P operator-(const P &r) const { return P(*this) -= r; } P operator-(const T &v) const { return P(*this) -= v; } P operator*(const P &r) const { return P(*this) *= r; } P operator*(const T &v) const { return P(*this) *= v; } P operator/(const P &r) const { return P(*this) /= r; } P operator%(const P &r) const { return P(*this) %= r; } P &operator+=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < int(r.size()); i++) (*this)[i] += r[i]; return *this; } P &operator+=(const T &r) { if(this->empty()) this->resize(1); (*this)[0] += r; return *this; } P &operator-=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < int(r.size()); i++) (*this)[i] -= r[i]; // shrink(); return *this; } P &operator-=(const T &r) { if(this->empty()) this->resize(1); (*this)[0] -= r; // shrink(); return *this; } P &operator*=(const T &v) { const int n = (int) this->size(); for(int k = 0; k < n; k++) (*this)[k] *= v; return *this; } P &operator*=(const P &r) { if(this->empty() || r.empty()) { this->clear(); return *this; } assert(get_mult() != nullptr); return *this = get_mult()(*this, r); } P &operator%=(const P &r) { return *this -= *this / r * r; } P operator-() const { P ret(this->size()); for(int i = 0; i < int(this->size()); i++) ret[i] = -(*this)[i]; return ret; } P &operator/=(const P &r) { if(this->size() < r.size()) { this->clear(); return *this; } int n = this->size() - r.size() + 1; return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n); } P pre(int sz) const { return P(begin(*this), begin(*this) + min((int) this->size(), sz)); } P operator>>(int sz) const { if((int)this->size() <= sz) return {}; P ret(*this); ret.erase(ret.begin(), ret.begin() + sz); return ret; } P operator<<(int sz) const { P ret(*this); ret.insert(ret.begin(), sz, T(0)); return ret; } P rev(int deg = -1) const { P ret(*this); if(deg != -1) ret.resize(deg, T(0)); reverse(begin(ret), end(ret)); return ret; } P diff() const { const int n = (int) this->size(); P ret(max(0, n - 1)); for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i); return ret; } P integral() const { const int n = (int) this->size(); P ret(n + 1); ret[0] = T(0); for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1); return ret; } // F(0) must not be 0 P inv(int deg = -1) const { assert(((*this)[0]) != T(0)); const int n = (int) this->size(); if(deg == -1) deg = n; P ret({T(1) / (*this)[0]}); for(int i = 1; i < deg; i <<= 1) { ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1); } return ret.pre(deg); } /* P inv_special(int k, int deg = -1) const { // ret = 0 + x/f_1 P ret({0, T(k)}); for(int i = 1; (i >> 1) < deg; i <<= 1) { // F(G_i(x)) P fg = (((-ret.pow(k, i << 1) + T(1)) * ret).pre(i << 1) * (-ret + T(1)).inv(i << 1)).pre(i << 1) * T(k).inv(); // G_(i + 1)(x) = G_i(x) - (F(G_i(x)) - x) / F'(G_i(x)) // G_(i + 1)(x) = G_i(x) - (F(G_i(x)) - x) / ((d/dx)F(G_i(x)) / (d/dx)G_i(x)) ret = (ret - ((fg - P{0, 1}) * ret.diff()).pre(i << 1) * (fg.diff()).inv(i << 1)).pre(i << 1); } return ret.pre(deg); } */ // F(0) must be 1 P log(int deg = -1) const { assert((*this)[0] == T(1)); const int n = (int) this->size(); if(deg == -1) deg = n; return (this->diff() * this->inv(deg)).pre(deg - 1).integral(); } P sqrt(int deg = -1) const { const int n = (int) this->size(); if(deg == -1) deg = n; if((*this)[0] == T(0)) { for(int i = 1; i < n; i++) { if((*this)[i] != T(0)) { if(i & 1) return {}; if(deg - i / 2 <= 0) break; auto ret = (*this >> i).sqrt(deg - i / 2) << (i / 2); if(int(ret.size()) < deg) ret.resize(deg, T(0)); return ret; } } return P(deg, 0); } P ret({T(1)}); T inv2 = T(1) / T(2); for(int i = 1; i < deg; i <<= 1) { ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2; } return ret.pre(deg); } // F(0) must be 0 P exp(int deg = -1) const { assert((*this)[0] == T(0)); const int n = (int) this->size(); if(deg == -1) deg = n; P ret({T(1)}); for(int i = 1; i < deg; i <<= 1) { ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1); } return ret.pre(deg); } P pow(int k, int deg = -1) const { const int n = (int) this->size(); if(deg == -1) deg = n; for(int i = 0; i < n; i++) { if((*this)[i] != T(0)) { T rev = T(1) / (*this)[i]; P C(*this * rev); P D(n - i); for(int j = i; j < n; j++) D[j - i] = C[j]; D = (D.log(deg) * T(k)).exp() * (*this)[i].pow(k); P E(deg); if(i * k > deg) return E; auto S = i * k; for(int j = 0; j + S < deg && j < D.size(); j++) E[j + S] = D[j]; return E; } } return *this; } P taylor_shift(T x) const { const int n = (int) this->size(); P p(n), q(n); for(int i = 0; i < n; i++) p[i] = facts(i) * (*this)[i]; for(int i = 0; i < n; i++) q[i] = ifacts(n - 1 - i) * x.pow(n - 1 - i); p *= q; p = p >> (n - 1); for(int i = 0; i < n; i++) p[i] *= ifacts(i); return p; } T get(int idx){ assert(idx >= 0); if(idx < int(this->size())) return (*this)[idx]; else return T(0); } void set(int idx, T x){ assert(idx >= 0); if(idx < int(this->size())) (*this)[idx] = x; else{ this->resize(idx + 1); T(0); } return; } T eval(T x) const { T r = 0, w = 1; for(auto &v : *this) { r += w * v; w *= x; } return r; } }; template<typename T> T BostanMori(FormalPowerSeries<T> P, FormalPowerSeries<T> Q, ll n){ assert(P.size() == Q.size()); if(n == 0) return P[0] / Q[0]; const int k = P.size(); FormalPowerSeries<T> R = Q; rep(i, k) if(i % 2 == 1) R[i] *= (T)-1; P *= R; Q *= R; FormalPowerSeries<T> U(k), V(k); if(n % 2 == 1) rep(i, k - 1) U[i] = P[2 * i + 1]; else rep(i, k) U[i] = P[2 * i]; rep(i, k) V[i] = Q[2 * i]; return BostanMori(U, V, n / 2); } // C = A * B in the full_relaxed way // c_i = \sigma_{j = 0}^{i} a_{j} b_{i - j} // Postulate: at the point of i, all of the a_j, b_j (0 <= j <= i) are known // O(N(longN)^2) // 5e5 * 5e5 -> 3300 ms // https://judge.yosupo.jp/submission/167521 template<typename T> void convolution_online(FormalPowerSeries<T>& a, FormalPowerSeries<T>& b, FormalPowerSeries<T>& c, int idx){ assert(int(c.size()) >= int(a.size()) + int(b.size()) - 1); int two = 1; rep(_, 30){ if(idx == 0 and two >= 2) break; if(!(idx % two == max(0, two - 2))) break; { FormalPowerSeries<T> a1(two), b1(two), c1; rep(i, two){a1[i] = a[(two - 1) + i]; b1[i] = b[idx - (two - 1) + i];} c1 = a1 * b1; rep(i, two * 2 - 1) c[idx + i] += c1[i]; } if(idx == (two - 1) * 2) break; { FormalPowerSeries<T> a2(two), b2(two), c2; rep(i, two){a2[i] = a[idx - (two - 1) + i]; b2[i] = b[(two - 1) + i];} c2 = a2 * b2; rep(i, two * 2 - 1) c[idx + i] += c2[i]; } two *= 2; } } namespace sparse{ // f^k (mod x^n)for sparse FPS f // O(N * M) (M is for # of terms of f) // Requirement : f0 = 1 vector<mint> pow(vector<pair<int, mint>> f, int N, mint k){ assert(int(f.size()) > 0); assert(f[0].first == 0); assert(f[0].second == (mint)1); vector<pair<int, mint>> f_prime; for(auto [n, c] : f) if(n > 0) f_prime.emplace_back(n - 1, c * n); vector<mint> F(N); vector<mint> F_prime(N); F[0] = 1; rep(n, N - 1){ mint res = 0; for(auto [m, c] : f){ if(m == 0) continue; if(m > n) break; res -= c * F_prime[n - m]; } for(auto [m, c] : f_prime){ if(m > n) break; res += k * c * F[n - m]; } F_prime[n] = res; F[n + 1] = res / (n + 1); } return F; } // exp(f) (mod x^n)for sparse FPS f // O(N * M) (M is for # of terms of f) // Requirement : f0 = 0 vector<mint> exp(vector<pair<int, mint>> f, int N){ assert(int(f.size()) > 0); assert(f[0].first > 0 or f[0].second == 0); vector<pair<int, mint>> f_prime; for(auto [n, c] : f) if(n > 0) f_prime.emplace_back(n - 1, c * n); vector<mint> F(N); vector<mint> F_prime(N); F[0] = 1; rep(n, N - 1){ mint res = 0; for(auto [m, c] : f_prime){ if(m > n) break; res += c * F[n - m]; } F_prime[n] = res; F[n + 1] = res / (n + 1); } return F; } // g / f (mod x^n for sparse FPS f and not sparse FPS g // O(N * M) (M is for # of terms of f) // Requirement : f0 = 1 vector<mint> quotient(vector<mint> g, vector<pair<int, mint>> f, int N){ assert(int(g.size()) == N); assert(int(f.size()) > 0); assert(f[0].first == 0); assert(f[0].second == (mint)1); vector<mint> F(N); F[0] = g[0]; for(int n = 1; n < N; n++){ mint res = g[n]; for(auto [m, c] : f){ if(m == 0) continue; if(m > n) break; res -= c * F[n - m]; } F[n] = res; } return F; } // log f (mod x^n) for sparse FPS f // O(N * M) (M is for # of terms of f) // Requirement : f0 = 1 vector<mint> log(vector<pair<int, mint>> f, int N){ assert(int(f.size()) > 0); assert(f[0].first == 0); assert(f[0].second == (mint)1); vector<mint> f_prime(N); for(auto [n, c] : f){ if(n == 0) continue; f_prime[n - 1] = c * n; } vector<mint> F_prime = quotient(f_prime, f, N); vector<mint> F(N); rep(n, N - 1) F[n + 1] = F_prime[n] / (n + 1); return F; } } // https://nyaannyaan.github.io/library/fps/berlekamp-massey.hpp // find series c such that a_n = c_1 a_(n-1) + .. + c_k a_(n-k) // need at least 2 * k terms template <typename T> vector<T> BerlekampMassey(const vector<T> &s) { const int N = (int)s.size(); vector<T> b, c; b.reserve(N + 1); c.reserve(N + 1); b.push_back(T(1)); c.push_back(T(1)); T y = T(1); for (int ed = 1; ed <= N; ed++) { int l = int(c.size()), m = int(b.size()); T x = 0; for (int i = 0; i < l; i++) x += c[i] * s[ed - l + i]; b.emplace_back(T(0)); m++; if (x == T(0)) continue; T freq = x / y; if (l < m) { auto tmp = c; c.insert(begin(c), m - l, T(0)); for (int i = 0; i < m; i++) c[m - 1 - i] -= freq * b[m - 1 - i]; b = tmp; y = x; } else { for (int i = 0; i < m; i++) c[l - 1 - i] -= freq * b[m - 1 - i]; } } reverse(begin(c), end(c)); return c; } template <typename T> T LinearRecurrence(const FormalPowerSeries<T>& s, long long n){ FormalPowerSeries<T> c = BerlekampMassey(s); auto t = c.size(); FormalPowerSeries<T> P = c * s; P = FormalPowerSeries<T>(P.begin(), P.begin() + t); P[t - 1] = 0; return BostanMori(P, c, n); }; // Thanks for maspy-san's submission // https://judge.yosupo.jp/submission/197702 template <typename T = mint> vector<vector<T>> convolution2d(vector<vector<T>>& f, vector<vector<T>>& g) { auto shape = [&](vector<vector<T>>& f) -> pair<int, int> { int H = len(f); int W = (H == 0 ? 0 : len(f[0])); return {H, W}; }; auto [H1, W1] = shape(f); auto [H2, W2] = shape(g); int H = H1 + H2 - 1; int W = W1 + W2 - 1; FormalPowerSeries<T> ff(H1 * W); FormalPowerSeries<T> gg(H2 * W); for(int x = 0; x < H1; x++) for(int y = 0; y < W1; y++) ff[W * x + y] = f[x][y]; for(int x = 0; x < H2; x++) for(int y = 0; y < W2; y++) gg[W * x + y] = g[x][y]; auto hh = convolution(ff, gg); vector<vector<T>> h(H, vector<T>(W)); for(int x = 0; x < H; x++) for(int y = 0; y < W; y++) h[x][y] = hh[W * x + y]; return h; } template<typename T> struct Merger{ int n; using P = FormalPowerSeries<T>; using Comp = std::function<bool(const P&, const P&)>; Comp comp = [](const P& a, const P& b){return a.size() > b.size();}; priority_queue<P, vector<P>, Comp> pq; Merger(int n = -1) : n(n), pq(comp){ pq.push(P{1}); } void add(P r){ pq.push(r); } P get(){ while(pq.size() > 1){ auto f = pq.top(); pq.pop(); auto g = pq.top(); pq.pop(); f *= g; if(n != -1) if(int(f.size()) > n) f.resize(n + 1); pq.push(f); } P res = pq.top(); return res; } }; void infer(mint a){ if(a == 0){cout << "0/1 "; return;} int p = a.mod(); long long u0 = 0, v0 = 1, w0 = a.val() * u0 + p * v0; long long u1 = 1, v1 = 0, w1 = a.val() * u1 + p * v1; while (w0*w0 >= p) { long long q = w0 / w1; u0 -= q * u1; v0 -= q * v1; w0 -= q * w1; u0 ^= u1; u1 ^= u0; u0 ^= u1; v0 ^= v1; v1 ^= v0; v0 ^= v1; w0 ^= w1; w1 ^= w0; w0 ^= w1; } if(u0 < 0){cout << '-'; u0 = abs(u0);} cout << w0 << '/' << u0 << ' '; } template<typename T> void infer(vector<T> v){for(auto& a : v) infer(a); cout << "\n";} using FPS = FormalPowerSeries<mint>; int main(){ long long n; int k; cin >> n >> k; int m = 2 * (k + 2); FPS a(m); a[0] = 1; a[1] = 1; for(int i = 2; i < m ; i++) a[i] = a[i - 1] + a[i - 2]; FPS b(m); rep(i, m) b[i] = a[i].pow(k); FPS s(m); s[0] = b[0]; rep(i, m - 1) s[i + 1] = s[i] + b[i + 1]; cout << LinearRecurrence(s, n - 1) << "\n"; return 0; }