結果

問題 No.2857 Div Array
ユーザー 👑 amentorimaruamentorimaru
提出日時 2024-08-25 15:37:01
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 37 ms / 2,000 ms
コード長 7,166 bytes
コンパイル時間 4,741 ms
コンパイル使用メモリ 251,172 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-08-25 15:37:08
合計ジャッジ時間 5,304 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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ファイルパターン 結果
other AC * 30
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 # 

#define ATCODER
#define _USE_MATH_DEFINES
#include <stdio.h>
#include <iostream>
#include <fstream>
#include <algorithm>
#include <vector>
#include <string>
#include <cassert>
#include <numeric>
#include <unordered_map>
#include <unordered_set>
#include <queue>
#include <math.h>
#include <climits>
#include <set>
#include <map>
#include <list>
#include <random>
#include <iterator>
#include <bitset>
#include <chrono>
#include <type_traits>
using namespace std;

using ll = long long;
using ld = long double;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;


#define FOR(i, a, b) for (ll i = (a); i < (b); i++)
#define REP(i, n) for (ll i = 0; i < (n); i++)
#define ROF(i, a, b) for (ll i = (b - 1); i >= (a); i--)
#define PER(i, n) for (ll i = n - 1; i >= 0; i--)
#define VL vector<ll>
#define VVL vector<vector<ll>>
#define VP vector<pair<ll, ll>>
#define LPQ(T) priority_queue<T, vector<T>, greater<T>>
#define all(i) begin(i), end(i)
#define SORT(i) sort(all(i))
#define EXISTBIT(x, i) (((x >> i) & 1) != 0)
#define CHMAX(n, v) n = n < v ? v : n
#define CHMIN(n, v) n = n > v ? v : n
#define MP(a, b) make_pair(a, b)
#define DET2(x1, y1, x2, y2) (x1) * (y2) - (x2) * (y1)
#define DET3(x1, y1, z1, x2, y2, z2, x3, y3, z3) (x1) * (y2) * (z3) + (x2) * (y3) * (z1) + (x3) * (y1) * (z2) - (z1) * (y2) * (x3) - (z2) * (y3) * (x1) - (z3) * (y1) * (x2)
#define INC(a)      \
  for (auto &v : a) \
    v++;
#define DEC(a)      \
  for (auto &v : a) \
    v--;
#define SQU(x) (x) * (x)

#ifdef ATCODER
#include <atcoder/all>
using namespace atcoder;
using mint = modint1000000007;
using mint2 = modint998244353;
#endif
template <typename T = ll>
vector<T> read(size_t n)
{
  vector<T> ts(n);
  for (size_t i = 0; i < n; i++)
    cin >> ts[i];
  return ts;
}

template <typename TV, const ll N>
void read_tuple_impl(TV &) {}
template <typename TV, const ll N, typename Head, typename... Tail>
void read_tuple_impl(TV &ts)
{
  get<N>(ts).emplace_back(*(istream_iterator<Head>(cin)));
  read_tuple_impl<TV, N + 1, Tail...>(ts);
}
template <typename... Ts>
decltype(auto) read_tuple(size_t n)
{
  tuple<vector<Ts>...> ts;
  for (size_t i = 0; i < n; i++)
    read_tuple_impl<decltype(ts), 0, Ts...>(ts);
  return ts;
}

using val = mint;
using val2 = mint2;
using func = ll;

val op(val a, val b)
{
  return a*b;
}
val e() { return 1; }

val2 op2(val2 a, val2 b)
{
  return a*b;
}
val2 e2() { return 1; }

val mp(func f, val a)
{
  return a + f;
}
func comp(func f, func g)
{
  return f + g;
}
func id() { return 0; }

ll di[4] = {1, 0, -1, 0};
ll dj[4] = {0, 1, 0, -1};
ll si[4] = {0, 3, 3, 0};
ll sj[4] = {0, 0, 3, 3};
// ll di[4] = { -1,-1,1,1 };
// ll dj[4] = { -1,1,-1,1 };
ll di8[8] = {0, -1, -1, -1, 0, 1, 1, 1};
ll dj8[8] = {-1, -1, 0, 1, 1, 1, 0, -1};

template<typename T = ll>
class Matrix {
public:
  Matrix(ll l, ll c = 1) {
    low = l;
    column = c;
    var.resize(l);
    for (ll i = 0; i < l; i++) {
      var[i].assign(c, T(0));
    }
  }

  T& operator()(int i, int j = 0) {
    return var[i][j];
  }

  Matrix<T> operator+=(Matrix<T> m) {
    for (ll i = 0; i < low; i++) {
      for (ll j = 0; j < column; j++) {
        var[i][j] += m(i, j);
      }
    }
    return *this;
  }

  Matrix<T> operator -() {
    for (ll i = 0; i < low; i++) {
      for (ll j = 0; j < column; j++) {
        var[i][j] *= T(-1);
      }
    }
    return *this;
  }

  Matrix<T> operator-=(Matrix<T> m) {
    *this += -m;
    return *this;
  }

  Matrix<T> operator*=(T s) {
    for (ll i = 0; i < low; i++) {
      for (ll j = 0; j < column; j++) {
        var[i][j] *= s;
      }
    }
    return *this;
  }

  Matrix<T> operator/=(T s) {
    for (ll i = 0; i < low; i++) {
      for (ll j = 0; j < column; j++) {
        var[i][j] /= s;
      }
    }
    return *this;
  }


  Matrix<T> operator+(Matrix<T> m) {
    Matrix<T> ans = *this;
    return ans += m;
  }

  Matrix<T> operator-(Matrix<T> m) {
    Matrix<T> ans = *this;
    return ans -= m;
  }

  Matrix<T> operator*(T s) {
    Matrix<T> ans = *this;
    return ans *= s;
  }

  Matrix<T> operator/(T s) {
    Matrix<T> ans = *this;
    return ans /= s;
  }

  Matrix<T> operator*(Matrix<T> m) {
    Matrix<T> ans(low, m.column);
    for (ll i = 0; i < low; i++) {
      for (ll j = 0; j < m.column; j++) {
        for (ll k = 0; k < m.low; k++) {
          ans.var[i][j] += ((var[i][k]) * (m(k, j)));
        }
      }
    }
    return ans;
  }

  Matrix<T> Gaussian() {
    auto ans = *this;
    vector<ll> f(column, -1);
    for (ll j = 0; j < column; j++) {
      for (ll i = 0; i < low; i++) {
        if (ans.var[i][j] == 0) continue;
        if (f[j] == -1) {
          bool ok = true;
          for (ll k = 0; k < j; k++) {
            ok = ok && i != f[k];
          }
          if (ok) {
            f[j] = i;
            break;
          }
        }
      }
      if (f[j] == -1) {
        continue;
      }
      T rev = 1 / ans(f[j], j);
      for (ll i = 0; i < low; i++) {
        if (ans.var[i][j] == 0)continue;
        if (i == f[j])continue;
        T mul = ans.var[i][j] * rev;
        for (ll k = j; k < column; k++) {
          ans.var[i][k] -= ans.var[f[j]][k] * mul;
        }
      }
    }
    return ans;
  }

  T Determinant() {
    auto g = Gaussian();
    T ans = 1;
    for (ll i = 0; i < low; i++) {
      ans *= g(i, i);
    }
    return ans;
  }

  Matrix<T> SubMatrix(ll lowS, ll lowC, ll colS, ll colC) {
    Matrix<T> ans(lowC, colC);
    for (ll i = 0; i < lowC; i++) {
      for (ll j = 0; j < colC; j++) {
        ans(i, j) = var[lowS + i][colS + j];
      }
    }
    return ans;
  }

  Matrix<T> Inverse() {
    Matrix<T> ex(low, column * 2);
    for (ll i = 0; i < low; i++) {
      ex(i, column + i) = T(1);
      for (ll j = 0; j < column; j++) {
        ex(i, j) = var[i][j];
      }
    }
    auto g = ex.Gaussian();
    auto s = g.SubMatrix(0, low, column, column);
    for (ll i = 0; i < low; i++) {
      if (g.var[i][i] == 0) {
        return Matrix<T>(0, 0);
      }
      T inv = 1 / g.var[i][i];
      for (ll j = 0; j < column; j++) {
        s(i, j) *= inv;
      }
    }
    return s;
  }

  vector<vector<T>> var;
  ll low;
  ll column;
};

template<typename T>
static Matrix<T> operator*(const T& t, const Matrix<T>& m) {
  return m * t;
}

template<typename T>
T Power(T var, ll p) {
  if (p == 1)
    return var;
  T ans = Power(var * var, p >> 1);
  if (p & 1)
    ans = ans * var;;
  return ans;
}

void solve()
{
  ll n,m,k;
  cin>>n>>m>>k;
  map<ll,ll> mp;
  REP(i,m){
    mp[m/(i+1)]++;
  }
  VL zat;
  unordered_map<ll,ll> rz;
  ll c=0;
  for(auto& [key,v]:mp){
    rz[key]=zat.size();
    zat.push_back(key);    
    c++;
  }
  Matrix<mint2> mf(c,1),mat(c,c);
  for(auto& [key,v]:mp){
    mf.var[rz[key]][0] = v;
  }
  REP(i,c){
    REP(j,c){
      ll v1=zat[i];
      ll v2=zat[j];
      if(abs(v1-v2)<=k){
        mat.var[i][j]=mp[v1];
      }
    }
  }
  if(n==1){
    cout<<m<<endl;
    return;
  }
  auto mpow=Power(mat,n-1);
  auto ans=mpow*mf;
  mint2 ansum=0;
  REP(i,c){
    ansum+=ans.var[i][0];
  }
  cout<<ansum.val()<<endl;
  return;
}

int main()
{
  ll t = 1;
  //cin >> t;
  while (t--)
  {
    solve();
  }
  return 0;
}
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