結果
| 問題 | No.2810 Have Another Go (Hard) |
| ユーザー |
👑  Nachia
|
| 提出日時 | 2024-07-12 21:58:17 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 69 ms / 3,000 ms |
| コード長 | 11,670 bytes |
| コンパイル時間 | 1,750 ms |
| コンパイル使用メモリ | 123,668 KB |
| 最終ジャッジ日時 | 2025-02-22 04:00:22 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 61 |
ソースコード
#ifdef NACHIA#define _GLIBCXX_DEBUG#else#define NDEBUG#endif#include <iostream>#include <string>#include <vector>#include <algorithm>#include <utility>#include <queue>#include <array>#include <cmath>using i64 = long long;using u64 = unsigned long long;#define rep(i,n) for(int i=0; i<int(n); i++)#define repr(i,n) for(int i=int(n)-1; i>=0; i--)const i64 INF = 1001001001001001001;const char* yn(bool x){ return x ? "Yes" : "No"; }template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }template<typename A> using nega_queue = std::priority_queue<A,std::vector<A>,std::greater<A>>;template<class R> auto ComparingBy(R f){ return [g=std::move(f)](auto l, auto r) -> bool { return g(l) < g(r); }; }#include <atcoder/modint>using Modint = atcoder::static_modint<998244353>;#include <iterator>#include <functional>template<class Elem> struct vec;template<class Iter>struct seq_view{using Ref = typename std::iterator_traits<Iter>::reference;using Elem = typename std::iterator_traits<Iter>::value_type;Iter a, b;Iter begin() const { return a; }Iter end() const { return b; }int size() const { return (int)(b-a); }seq_view(Iter first, Iter last) : a(first), b(last) {}seq_view sort() const { std::sort(a, b); return *this; }Ref& operator[](int x){ return *(a+x); }template<class F = std::less<Elem>, class ret = vec<int>> ret sorti(F f = F()) const {ret x(size()); for(int i=0; i<size(); i++) x[i] = i;x().sort([&](int l, int r){ return f(a[l],a[r]); });return x;}template<class ret = vec<Elem>> ret col() const { return ret(begin(), end()); }template<class F = std::equal_to<Elem>, class ret = vec<std::pair<Elem, int>>>ret rle(F eq = F()) const {auto x = ret();for(auto& a : (*this)){if(x.size() == 0 || !eq(x[x.size()-1].first, a)) x.emp(a, 1); else x[x.size()-1].second++;} return x;}template<class F> seq_view sort(F f) const { std::sort(a, b, f); return *this; }Iter uni() const { return std::unique(a, b); }Iter lb(const Elem& x) const { return std::lower_bound(a, b, x); }Iter ub(const Elem& x) const { return std::upper_bound(a, b, x); }int lbi(const Elem& x) const { return lb(x) - a; }int ubi(const Elem& x) const { return ub(x) - a; }seq_view bound(const Elem& l, const Elem& r) const { return { lb(l), lb(r) }; }template<class F> Iter lb(const Elem& x, F f) const { return std::lower_bound(a, b, x, f); }template<class F> Iter ub(const Elem& x, F f) const { return std::upper_bound(a, b, x, f); }template<class F> Iter when_true_to_false(F f) const {if(a == b) return a;return std::lower_bound(a, b, *a,[&](const Elem& x, const Elem&){ return f(x); });}seq_view same(Elem x) const { return { lb(x), ub(x) }; }template<class F> auto map(F f) const {vec<typename Iter::value_type> r;for(auto& x : *this) r.emp(f(x));return r;}Iter max() const { return std::max_element(a, b); }Iter min() const { return std::min_element(a, b); }template<class F = std::less<Elem>>Iter min(F f) const { return std::min_element(a, b, f); }seq_view rev() const { std::reverse(a, b); return *this; }};template<class Elem>struct vec {using Base = typename std::vector<Elem>;using Iter = typename Base::iterator;using CIter = typename Base::const_iterator;using View = seq_view<Iter>;using CView = seq_view<CIter>;vec(){}explicit vec(int n, const Elem& value = Elem()) : a(0<n?n:0, value) {}template <class I2> vec(I2 first, I2 last) : a(first, last) {}vec(std::initializer_list<Elem> il) : a(std::move(il)) {}vec(Base b) : a(std::move(b)) {}operator Base() const { return a; }Iter begin(){ return a.begin(); }CIter begin() const { return a.begin(); }Iter end(){ return a.end(); }CIter end() const { return a.end(); }int size() const { return a.size(); }bool empty() const { return a.empty(); }Elem& back(){ return a.back(); }const Elem& back() const { return a.back(); }vec sortunied(){ vec x = *this; x().sort(); x.a.erase(x().uni(), x.end()); return x; }Iter operator()(int x){ return a.begin() + x; }CIter operator()(int x) const { return a.begin() + x; }View operator()(int l, int r){ return { (*this)(l), (*this)(r) }; }CView operator()(int l, int r) const { return { (*this)(l), (*this)(r) }; }View operator()(){ return (*this)(0,size()); }CView operator()() const { return (*this)(0,size()); }Elem& operator[](int x){ return a[x]; }const Elem& operator[](int x) const { return a[x]; }Base& operator*(){ return a; }const Base& operator*() const { return a; }vec& push(Elem args){a.push_back(std::move(args));return *this;}template<class... Args>vec& emp(Args &&... args){a.emplace_back(std::forward<Args>(args) ...);return *this;}template<class Range>vec& app(Range& x){ for(auto& v : a) emp(v); }Elem pop(){Elem x = std::move(a.back());a.pop_back(); return x;}bool operator==(const vec& r) const { return a == r.a; }bool operator!=(const vec& r) const { return a != r.a; }bool operator<(const vec& r) const { return a < r.a; }bool operator<=(const vec& r) const { return a <= r.a; }bool operator>(const vec& r) const { return a > r.a; }bool operator>=(const vec& r) const { return a >= r.a; }vec<vec<Elem>> pile(int n) const { return vec<vec<Elem>>(n, *this); }template<class F> vec& filter(F f){int p = 0;for(int q=0; q<size(); q++) if(f(a[q])) std::swap(a[p++],a[q]);a.resize(p); return *this;}private: Base a;};template<class IStr, class U, class T>IStr& operator>>(IStr& is, vec<std::pair<U,T>>& v){ for(auto& x:v){ is >> x.first >> x.second; } return is; }template<class IStr, class T>IStr& operator>>(IStr& is, vec<T>& v){ for(auto& x:v){ is >> x; } return is; }template<class OStr, class T>OStr& operator<<(OStr& os, const vec<T>& v){for(int i=0; i<v.size(); i++){if(i){ os << ' '; } os << v[i];} return os;}template<class OStr, class U, class T>OStr& operator<<(OStr& os, const vec<std::pair<U,T>>& v){for(int i=0; i<v.size(); i++){if(i){ os << ' '; } os << '(' << v[i].first << ',' << v[i].second << ')';} return os;}#include <cassert>namespace nachia{template<class Elem>struct MatrixModulo{private:int h;int w;std::vector<Elem> elems;public:MatrixModulo(int new_h=0, int new_w=0): h(new_h), w(new_w), elems(h*w, Elem(0)){}MatrixModulo(const MatrixModulo &) = default;int numRow() const { return h; }int numColumn() const { return w; }int height() const { return numRow(); }int width() const { return numColumn(); }typename std::vector<Elem>::iterator operator[](int y){ return elems.begin() + (y*w); }typename std::vector<Elem>::const_iterator operator[](int y) const { return elems.begin() + (y*w); }static MatrixModulo Identity(int n){auto res = MatrixModulo(n,n);for(int i=0; i<n; i++) res[i][i]=Elem(1);return res;}MatrixModulo transposed() const {auto res = MatrixModulo(w,h);for(int i=0; i<h; i++) for(int j=0; j<w; j++) res[j][i] = elems[i*w+j];return res;}void swapColumns(int x1, int x2){assert(0 <= x1 && x1 < numColumn());assert(0 <= x2 && x2 < numColumn());for(int y=0; y<numRow(); y++) std::swap((*this)[y][x1], (*this)[y][x2]);}void swapRows(int y1, int y2){assert(0 <= y1 && y1 < numRow());assert(0 <= y2 && y2 < numRow());for(int x=0; x<numColumn(); x++) std::swap((*this)[y1][x], (*this)[y2][x]);}MatrixModulo operator*(const MatrixModulo& r) const {assert(width() == r.height());auto res = MatrixModulo(h, r.w);for(int i=0; i<h; i++) for(int j=0; j<w; j++) for(int k=0; k<r.w; k++){res[i][k] += (*this)[i][j] * r[j][k];}return res;}std::vector<Elem> operator*(const std::vector<Elem>& r) const {assert(width() == int(r.size()));auto res = std::vector<Elem>(h);for(int i=0; i<h; i++) for(int j=0; j<w; j++){res[i] += (*this)[i][j] * r[j];}return res;}Elem det() const {assert(height() == width());MatrixModulo g = *this;Elem ans = 1;for(int i=0; i<h; i++){int tg = -1;for(int j=i; j<h; j++){ if(g[j][i].val() != 0) tg = j; }if(tg == -1) return 0;if(tg != i) ans = -ans;for(int j=0; j<h; j++) std::swap(g[i][j], g[tg][j]);tg = i;ans *= g[i][i];Elem const_coeff = g[i][i].inv();for(int j=0; j<h; j++) g[i][j] *= const_coeff;for(int j=i+1; j<h; j++) for(int k=h-1; k>=i; k--) g[j][k] -= g[j][i] * g[i][k];}return ans;}int rank() const {if(height() == 0 || width() == 0) return 0;MatrixModulo g = *this;int y = 0;for(int d=0; d<w; d++){if(y == h) break;int tg = -1;for(int i=y; i<h; i++){ if(g[i][d].val() != 0){ tg = i; break; } }if(tg == -1) continue;for(int j=d; j<w; j++) std::swap(g[y][j], g[tg][j]);tg = y;Elem const_coeff = g[y][d].inv();for(int j=d; j<w; j++) g[y][j] *= const_coeff;for(int i=y+1; i<h; i++) for(int j=w-1; j>=d; j--) g[i][j] -= g[i][d] * g[y][j];y++;}return y;}MatrixModulo pow(unsigned long long i){auto a = *this;auto res = Identity(height());while(i){if(i%2) res = res * a;a = a * a; i /= 2;}return res;}};} // namespace nachiausing namespace std;void testcase(){using Mat = nachia::MatrixModulo<Modint>;Mat X(6,6);rep(i,5) X[i][i+1] += 1;rep(i,6) X[i][0] += 1;vec<Mat> G; G.push(X);rep(i,60) G.push(G.back() * G.back());auto Gpow = [&](i64 n) -> Mat {auto cy = Mat::Identity(6);rep(b,60) if(n & (1ll << b)) cy = cy * G[b];return cy;};auto GpowV = [&](i64 n, vector<Modint> v) -> vector<Modint> {rep(b,60) if(n & (1ll << b)) v = G[b].transposed() * v;return v;};i64 N, M; cin >> N >> M;i64 K; cin >> K;vec<i64> C(K); cin >> C;auto cy = Gpow(N);auto cy2 = Mat(12, 12);rep(i,6) rep(j,6) cy2[i+6][j+6] += cy[i][j];rep(i,6) rep(j,5) cy2[i][j+1] += cy[i][j+1];rep(i,6) cy2[i][6] += cy[i][0];cy2 = cy2.pow(M-1);for(i64 c : C){vector<Modint> A(12);vector<Modint> sa(6); sa[0] = 1;sa = GpowV(c, sa);//for(auto a : sa) cout << a.val() << " ";//cout << endl;rep(i,6) A[i] = sa[i];swap(A[0], A[6]);A = cy2.transposed() * A;sa = vector<Modint>(A.begin() + 6, A.begin() + 12);//for(auto a : sa) cout << a.val() << " ";//cout << endl;sa = GpowV(N-c-1, sa);Modint ans = 0;rep(i,6) ans += sa[i] * (6-i);cout << ans.val() << '\n';}}int main(){ios::sync_with_stdio(false); cin.tie(nullptr);testcase();return 0;}