結果

問題 No.2670 Sum of Products of Interval Lengths
ユーザー cureskolcureskol
提出日時 2024-03-05 20:30:38
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 428 ms / 2,000 ms
コード長 13,485 bytes
コンパイル時間 5,438 ms
コンパイル使用メモリ 267,324 KB
実行使用メモリ 16,440 KB
最終ジャッジ日時 2024-03-05 20:30:53
合計ジャッジ時間 14,185 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge12
このコードへのチャレンジ
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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 423 ms
15,716 KB
testcase_01 AC 415 ms
16,440 KB
testcase_02 AC 416 ms
16,440 KB
testcase_03 AC 426 ms
16,440 KB
testcase_04 AC 415 ms
16,440 KB
testcase_05 AC 418 ms
16,440 KB
testcase_06 AC 428 ms
16,440 KB
testcase_07 AC 414 ms
15,716 KB
testcase_08 AC 413 ms
15,716 KB
testcase_09 AC 425 ms
15,716 KB
testcase_10 AC 414 ms
15,716 KB
testcase_11 AC 425 ms
15,716 KB
testcase_12 AC 415 ms
16,440 KB
testcase_13 AC 414 ms
16,440 KB
testcase_14 AC 428 ms
16,440 KB
testcase_15 AC 416 ms
16,440 KB
testcase_16 AC 416 ms
16,440 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#pragma region template
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ld = long double;
using vi = vector<int>;
using vll = vector<ll>;
using pi = pair<int, int>;
using pll = pair<ll, ll>;

#define overload2(a, b, c, ...) c
#define overload3(a, b, c, d, ...) d
#define overload4(a, b, c, d, e, ...) e
#define overload5(a, b, c, d, e, f, ...) f

#define TYPE1(T) template <typename T>
#define TYPE2(T, U) template <typename T, typename U>
#define TYPE(...) overload2(__VA_ARGS__, TYPE2, TYPE1)(__VA_ARGS__)
#define TYPES1(T) template <typename... T>
#define TYPES2(H, T) template <typename H, typename... T>
#define TYPES(...) overload2(__VA_ARGS__, TYPES2, TYPES1)(__VA_ARGS__)

#define REP4(i, s, n, d) for (int i = (s); i < (n); i += (d))
#define REP3(i, s, n) REP4(i, s, n, 1)
#define REP2(i, n) REP3(i, 0, n)
#define REP1(n) REP2(tomato, n)
#define REP(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)

#define RREP4(i, n, s, d) for (int i = (n)-1; i >= (s); i -= (d))
#define RREP3(i, n, s) RREP4(i, n, s, 1)
#define RREP2(i, n) RREP3(i, n, 0)
#define RREP1(n) RREP2(tomato, n)
#define RREP(...)                                                              \
  overload4(__VA_ARGS__, RREP4, RREP3, RREP2, RREP1)(__VA_ARGS__)

#define FOR4(a, b, c, d, v) for (auto [a, b, c, d] : v)
#define FOR3(a, b, c, v) for (auto [a, b, c] : v)
#define FOR2(a, b, v) for (auto [a, b] : v)
#define FOR1(a, v) for (auto a : v)
#define FOR(...) overload5(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)

#define AFOR4(a, b, c, d, v) for (auto &[a, b, c, d] : v)
#define AFOR3(a, b, c, v) for (auto &[a, b, c] : v)
#define AFOR2(a, b, v) for (auto &[a, b] : v)
#define AFOR1(a, v) for (auto &a : v)
#define AFOR(...)                                                              \
  overload5(__VA_ARGS__, AFOR4, AFOR3, AFOR2, AFOR1)(__VA_ARGS__)

#define CFOR4(a, b, c, d, v) for (const auto &[a, b, c, d] : v)
#define CFOR3(a, b, c, v) for (const auto &[a, b, c] : v)
#define CFOR2(a, b, v) for (const auto &[a, b] : v)
#define CFOR1(a, v) for (const auto &a : v)
#define CFOR(...)                                                              \
  overload5(__VA_ARGS__, CFOR4, CFOR3, CFOR2, CFOR1)(__VA_ARGS__)

#define PFOR(v)                                                                \
  for (bool f = true; (f ? exchange(f, false) : next_permutation(ALL(v)));)

#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define SORT(v) sort(ALL(v))
#define RSORT(v) sort(RALL(v))
#define REVERSE(v) reverse(ALL(v))
#define UNIQUE(v) SORT(v), v.erase(unique(ALL(v)), v.end())
#define SZ(v) int(v.size())
#define MAX(v) *max_element(ALL(v))
#define MIN(v) *min_element(ALL(v))
template <typename T>
conditional_t<is_same_v<T, int>, ll, T> SUM(const vector<T> &v) {
  return accumulate(ALL(v), conditional_t<is_same_v<T, int>, ll, T>(0));
}

TYPES(T) void input(T &...a) { (cin >> ... >> a); }
#define DECLARE(T, ...)                                                        \
  T __VA_ARGS__;                                                               \
  input(__VA_ARGS__);
#define INT(...) DECLARE(int, __VA_ARGS__)
#define STR(...) DECLARE(string, __VA_ARGS__)
#define LL(...) DECLARE(long long, __VA_ARGS__)
#define CHR(...) DECLARE(char, __VA_ARGS__)
#define DBL(...) DECLARE(double, __VA_ARGS__)
#define VI(n, v)                                                               \
  vi v(n);                                                                     \
  cin >> v;
#define VLL(n, v)                                                              \
  vll v(n);                                                                    \
  cin >> v;
#define VS(n, s)                                                               \
  vector<string> s(n);                                                         \
  cin >> s;

TYPE(T) istream &operator>>(istream &is, vector<T> &v) {
  for (auto &a : v)
    cin >> a;
  return is;
}
TYPE(T) ostream &operator<<(ostream &os, const vector<T> &v) {
  if (&os == &cerr)
    os << "[";
  REP (i, v.size()) {
    os << v[i];
    if (i + 1 < v.size())
      os << (&os == &cerr ? "," : " ");
  }
  if (&os == &cerr)
    os << "]";
  return os;
}
TYPE(T, S) istream &operator>>(istream &is, pair<T, S> &p) {
  cin >> p.first >> p.second;
  return is;
}

#ifdef __DEBUG
#include <debug>
#else
#define debug(...) void(0)
#endif

void print() { cout << '\n'; }
TYPES(T, Ts) void print(const T &a, const Ts &...b) {
  cout << a;
  (cout << ... << (cout << ' ', b));
  cout << '\n';
}

TYPE(T) using pq = priority_queue<T>;
TYPE(T) using pqg = priority_queue<T, vector<T>, greater<T>>;
TYPE(T) T pick(queue<T> &que) {
  assert(que.size());
  T a = que.front();
  que.pop();
  return a;
}
TYPE(T) T pick(pq<T> &que) {
  assert(que.size());
  T a = que.top();
  que.pop();
  return a;
}
TYPE(T) T pick(pqg<T> &que) {
  assert(que.size());
  T a = que.top();
  que.pop();
  return a;
}
TYPE(T) T pick(stack<T> &sta) {
  assert(sta.size());
  T a = sta.top();
  sta.pop();
  return a;
}
TYPE(T) void clear(T &v) { v = decltype(v)(); }

string YES(bool f = true) { return (f ? "YES" : "NO"); }
string Yes(bool f = true) { return (f ? "Yes" : "No"); }
string yes(bool f = true) { return (f ? "yes" : "no"); }

constexpr int INF = 1e9 + 7;
constexpr ll LINF = ll(1e18) + 7;
constexpr ld EPS = 1e-10;

vi iota(int n) {
  vi a(n);
  iota(ALL(a), 0);
  return a;
}
TYPE(T) vector<pair<T, int>> query_sort(const vector<T> &v) {
  vector<pair<T, int>> res(v.size());
  REP (i, v.size())
    res[i] = {v[i], i};
  SORT(res);
  return res;
}
TYPE(T) void add(vector<T> &v, T a = 1) {
  AFOR (p, v)
    p += a;
}
TYPE(T) T rev(T a) {
  REVERSE(a);
  return a;
}
TYPE(T) void fin(T a) {
  cout << a << '\n';
  exit(0);
}
TYPE(T) bool chmax(T &a, T b) { return (a < b && (a = b, true)); }
TYPE(T) bool chmin(T &a, T b) { return (a > b && (a = b, true)); }
TYPES(T, Ns) auto make_vector(T x, int n, Ns... ns) {
  if constexpr (sizeof...(ns) == 0)
    return vector<T>(n, x);
  else
    return vector(n, make_vector<T>(x, ns...));
}
bool in(const ll S, const int a) { return (S >> a) & 1; }
int popcount(const ll S) { return __builtin_popcountll(S); }
int digit(char c) { return (c >= '0' and c <= '9' ? c - '0' : -1); }
ll sqrtll(ll a) {
  for (ll b = sqrt(a); b * b <= a; b++)
    if (b * b == a)
      return b;
  for (ll b = sqrt(a); b >= 0 and b * b >= a; b--)
    if (b * b == a)
      return b;
  return -1;
}
#pragma endregion template

#include <atcoder/convolution>
#include <atcoder/modint>
using namespace atcoder;
using mint = modint998244353;
namespace atcoder {
ostream &operator<<(ostream &os, mint a) {
  os << a.val();
  return os;
}
istream &operator>>(istream &is, mint &a) {
  long long b;
  is >> b;
  a = b;
  return is;
}
} // namespace atcoder

#define REP_(i,n) for(int i=0;i<(n);i++)
template<typename T,int MX>
struct FormalPowerSeries:vector<T>{
  using FPS=FormalPowerSeries;
  using vector<T>::resize;
  using vector<T>::size;
  using vector<T>::at;
  using vector<T>::assign;
  using vector<T>::vector;
  using vector<T>::begin;
  using vector<T>::end;
  using vector<T>::back;
  using vector<T>::pop_back;
  using value_type=T;

  void strict(int n){ if(size()>n)resize(n); }
  void shrink(){ while(size() and back()==0)pop_back(); }

  FormalPowerSeries(const vector<T>&f){
    int n=min(MX,int(f.size()));
    resize(n);
    REP_(i,n)at(i)=f[i];
    shrink();
  }

  static FPS unit(){ return {1}; }
  static FPS x(){ return {0,1}; }
#pragma region operator
  FPS operator-()const{
    FPS g=*this;
    for(T&a:g)a=-a;
    return g;
  }
  
  FPS &operator+=(const FPS&g){
    if(size()<g.size())resize(g.size());
    REP_(i,g.size())at(i)+=g[i];
    return *this;
  }
  FPS operator+(const FPS &g)const{return FPS(*this)+=g;}

  FPS &operator+=(const T &a){
    if(!size())resize(1);
    at(0)+=a;
    return *this;
  }
  FPS operator+(const T& a)const{return FPS(*this)+=a;}
  friend FPS operator+(const T&a,const FPS&f){return f+a;}

  FPS &operator-=(const FPS &g){
    if(size()<g.size())resize(g.size());
    REP_(i,g.size())at(i)-=g[i];
    return *this;
  }
  FPS operator-(const FPS &g)const{return FPS(*this)-=g;}

  FPS &operator-=(const T &a){
    if(!size())resize(1);
    at(0)-=a;
    return *this;
  }
  FPS operator-(const T& a){return FPS(*this)-=a;}
  friend FPS operator-(const T&a,const FPS&f){return a+(-f);}
  
  FPS operator*(const FPS&g)const{ return FPS(convolution(*this,g)); }
  FPS&operator*=(const FPS&g){ return (*this)=(*this)*g; }

  FPS&operator*=(const T &a){
    REP_(i,size())at(i)*=a;
    return *this;
  }
  FPS operator*(const T &a)const{ return FPS(*this)*=a; }
  friend FPS operator*(const T&a,const FPS&f){return f*a;}

  FPS operator/(const FPS g)const{ return (*this)*g.inv(); }
  FPS&operator/=(const FPS&g){ return (*this)=(*this)/g; }

  FPS&operator/=(const T &a){ return *this *= a.inv(); }
  FPS operator/(const T &a){ return  FPS(*this)/=a; }

  FPS&operator<<=(const int d){
    if(d>=MX)return *this=FPS(0);
    resize(min(MX,int(size())+d));
    for(int i=int(size())-1-d;i>=0;i--)
      at(i+d)=at(i);
    for(int i=d-1;i>=0;i--)at(i)=0;
    return *this;
  }
  FPS operator<<(const int d)const{ return FPS(*this)<<=d; }
  FPS&operator>>=(const int d){
    if(d>=size())return *this=FPS(0);
    for(int i=d;i<size();i++)
      at(i-d)=at(i);
    strict(int(size())-d);
    return *this;
  }
  FPS operator>>(const int d)const{ return FPS(*this)>>=d; }
#pragma endregion operator

  FPS pre(int n)const{
    if(size()<=n)return *this;
    return FPS(begin(),begin()+n);
  }

  FPS inv(int SZ=MX)const{
    assert(size() and at(0)!=0);
    FPS res(1,at(0).inv());
    for(int n=0;(1<<n)<SZ;n++){
      res *= (2- (res*pre(1<<(n+1))).pre(1<<(n+1)));
      res.strict(1<<(n+1));
    }
    return res.pre(SZ);
  }

  FPS pow(long long n)const{
    assert(n>=0);
    if(n==0)return unit();
    if(n==1)return *this;

    FPS now=*this;
    now.shrink();
    if(!now.size())return now;
    int d;
    for(d=0;d<now.size() and now[d]==0;d++){}
    if(d>=(MX+n-1)/n)return FPS(0);
    now >>= d;
    d *= n;
    if(at(0)==1)return exp(n*log(now))<<d;
    FPS res=unit();
    while(n){
      if(n&1)res*=now;
      now*=now;
      n>>=1;
    }
    return res<<d;
  }

  FPS separate(int n){
    if(size()<=n)return FPS(0);
    FPS f_2(size()-n);
    for(int i=n;i<size();i++)f_2[i-n]=at(i);
    strict(n);
    return f_2;
  }

  FPS operator()(FPS g)const{
    assert(!g.size() or g[0]==0); // 自身が多項式なら g[0]!=0 でも良い
    if(size()==0)return *this;
    if(size()==1)return FPS(1,at(0));
    if(size()==2)return FPS(at(0)+at(1)*g);

    int m=sqrt(MX/20);
    FPS&g1=g;
    FPS g2=g1.separate(m);

    int z;
    for(z=1;z<g1.size() and g1[z]==0;z++){}
    if(z==g1.size()){
      FPS res(0),
          g2pow=FPS::unit();
      for(int i=0;i*m<MX and i<size();i++,g2pow*=g2)
        res += at(i) * g2pow<<(i*m);
      return res;
    }
    
    auto rec=[&](auto rec,int l,int d){
      if(d==0 or l>=size())return FPS(0);
      if(d==1)return FPS(1,at(l));
      if(d==2)return at(l) + (l+1<size()?at(l+1)*g1:FPS(0));
      FPS f1=rec(rec,l,d>>1);
      FPS f2=rec(rec,l+(d>>1),d-(d>>1));
      f2 *= g1.pow(d>>1);
      return f1+f2;
    };
    FPS res = rec(rec,0,size());

    FPS dfg=res,
        g1inv=(differential(g)>>(--z)).inv(),
        g2pow=FPS::unit();
    T factinv=1;
    
    for(int i=1;i*m<MX;i++){
      dfg=(differential(dfg)>>z)*g1inv;
      dfg.strict(MX-m*i);
      (g2pow*=g2).strict(MX-m*i);
      factinv /= i;
      res += factinv * (dfg * g2pow) << (m*i);
    }
    return res;
  }
  T operator()(T a)const{
    T res=0,b=1;
    for(int i=0;i<size();i++,b*=a)
      res += at(i)*b;
    return res;
  }

  void taylor_shift(T c){
    shrink();
    if(size()<=1 or c==0)return;
    int n=size();
    T fact=1;
    REP_(i,n){
      if(i)fact*=i;
      at(i)*=fact;
    }
    reverse(begin(),end());
    *this *= exp(c).pre(n);
    strict(n);
    reverse(begin(),end());
    T finv=fact.inv();
    for(int i=n-1;i>=0;i--){
      at(i)*=finv;
      finv *= i;
    }
  }

  static FPS differential(FPS f){
    if(f.size()<=1)return FPS(0);
    REP_(i,f.size()-1)f[i]=(i+1)*f[i+1];
    f.resize(f.size()-1);
    return f;
  }
  static FPS integral(FPS f){
    if(f.size()<MX)f.resize(f.size()+1);
    for(int i=f.size()-1;i>0;i--)f[i]=f[i-1]/i;
    f[0]=0;
    return f;
  }

  static FPS log(const FPS&f){
    assert(f.size() and f[0]==1);
    return integral(differential(f)/f);
  }
  static FPS exp(const FPS f){
    if(!f.size())return unit();
    assert(f[0]==0);
    FPS res=unit();
    for(int n=0;(1<<n)<MX;n++){
      res *= (f.pre(1<<(n+1))+1-log(res).pre(1<<(n+1)));
      res.strict(1<<(n+1));
    }
    return res;
  }
  static FPS exp(const T n){
    if(n==0)return unit();
    FPS res(MX,1);
    for(int i=1;i<MX;i++)res[i]=res[i-1]*n/i;
    return res;
  }
};
#undef REP_
using FPS = FormalPowerSeries<mint, 200001>;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  FPS a = FPS(vector<mint>{1, -1});
  FPS f = FPS::x() / (a * a);
  f *= -1;

  debug(f);

  FPS g = f / (FPS::unit() - f);
  g *= -1;

  debug(g);

  // REP (i, g.size())
  //   g[i] = 2 * i - g[i];

  debug(g);
  LL(n, m);

  REP (i, g.size())
    g[i] *= std::max(m - i + 1, 0LL);

  debug(g);

  g = g / (1 - g);
  debug(g);

  std::cout << g[n] << '\n';
}
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