#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include using ull = unsigned long long; using namespace std; using namespace atcoder; using vst = vector; using ll = long long; using ld = long double; using P = pair; using vl = vector; using vvl = vector; using vP = vector

; #define rep(i, n) for (ll i = 0; i < n; i++) #define repp(i,k,n) for (ll i = k; i < n; i++) #define per(i,s,e) for(ll i = s; i >= e; i--) #define all(v) v.begin(),v.end() #define yesno(a) a ? cout << "Yes" << '\n' : cout << "No" << '\n' #define YESNO(a) a ? cout << "YES" << '\n' : cout << "NO" << '\n' #define UNOmap unordered_map #define UNOset unordered_set #define chmax(a,b) a=max(a,b) #define chmin(a,b) a=min(a,b) #define debug(x) cerr << #x << " = " << x << '\n' templatevoid in(T&... a){(cin >> ... >> a);} templatevoid out(const T& a, const Ts&... b){cout << a;((cout << ' ' << b), ...);cout << '\n';} template void vin2(vector &u,vector &v){for(ll i = 0; i < (ll)v.size(); i++) in(u[i],v[i]);} template void vin(vector &v){for(ll i = 0; i < (ll)v.size(); i++)in(v[i]);} template void vout(vector &v){for(ll i = 0; i < (ll)v.size(); i++) cout << v[i] << ' ';cout << "\n";} ll INF = 1152921504606846976;ll MOD =998244353; ll MOD1 =1000000007; /* INF = 1LL << 60 */ #define sl(...) ll __VA_ARGS__; in(__VA_ARGS__) using mint = modint998244353; using mint1 = modint1000000007; using mintn = modint; using vm = vector; using vvm = vector; vl dx = {0,0,1,-1}, dy = {1,-1,0,0}; //---------------------------------------------- template< class T > struct Matrix { vector< vector< T > > A; Matrix() {} Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {} Matrix(size_t n) : A(n, vector< T >(n, 0)) {}; size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const vector< T > &operator[](int k) const { return (A.at(k)); } inline vector< T > &operator[](int k) { return (A.at(k)); } static Matrix I(size_t n) { Matrix mat(n); for(int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); vector< vector< T > > C(n, vector< T >(m, 0)); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) for(int k = 0; k < p; k++) C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); A.swap(C); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::I(height()); while(k > 0) { if(k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return (*this); } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); } friend ostream &operator<<(ostream &os, Matrix &p) { size_t n = p.height(), m = p.width(); for(int i = 0; i < n; i++) { os << "["; for(int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "]\n" : ","); } } return (os); } T determinant() { Matrix B(*this); assert(width() == height()); T ret = 1; for(int i = 0; i < width(); i++) { int idx = -1; for(int j = i; j < width(); j++) { if(B[j][i] != 0) idx = j; } if(idx == -1) return (0); if(i != idx) { ret *= -1; swap(B[i], B[idx]); } ret *= B[i][i]; T vv = B[i][i]; for(int j = 0; j < width(); j++) { B[i][j] /= vv; } for(int j = i + 1; j < width(); j++) { T a = B[j][i]; for(int k = 0; k < width(); k++) { B[j][k] -= B[i][k] * a; } } } return (ret); } }; int main(){ ios::sync_with_stdio(false);cin.tie(nullptr);cout< Mt(M,M); rep(i,M) rep(j,M){ Mt[i][j] =0; if(abs(j-i) <= K) Mt[i][j]=1; } Matrix Nt(M,1); repp(i,1,M+1){ Nt[M/i-1][0]++; } rep(i,M) rep(j,M){ Mt[i][j] =0; if(abs(j-i) <= K) Mt[i][j]=Nt[i][0]; } Mt ^=N-1; rep(i,M){ rep(j,M){ //out(Mt[i][j].val()); } } Mt *= Nt; mint ans = 0; rep(i,M){ //out(Mt[i][0].val()); ans += Mt[i][0]; } out(ans.val()); }