#include using namespace std; #define int long long #define REP(i, n) for (long long i = 0, max_i = (n); i < max_i; i++) #define REPI(i, a, b) for (long long i = (a), max_i = (b); i < max_i; i++) #define ALL(obj) begin(obj), end(obj) #define RALL(obj) rbegin(obj), rend(obj) #define fi first #define se second using ii = pair; vector dirs = { {1, 0}, {0, 1}, {-1, 0}, {0, -1}, // 4方向 {1, 1}, {-1, 1}, {-1, -1}, {1, -1}, // 斜め {0, 0}, // 自身 }; template inline bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } return false; } template vector make_vec(size_t n, S x) { return vector(n, x); } template auto make_vec(size_t n, Ts... ts) { return vector(ts...))>(n, make_vec(ts...)); } // debug template ostream& operator<<(ostream& s, vector& d) { REP (i, d.size()) s << d[i] << (i == d.size() - 1 ? "" : " "); return s; } template ostream& operator<<(ostream& s, vector>& d) { REP (i, d.size()) s << d[i] << (i == d.size() - 1 ? "" : "\n"); return s; } template ostream& operator<<(ostream& s, pair& p) { s << "{" << p.first << ", " << p.second << "}"; return s; } template ostream& operator<<(ostream& s, map m) { for (auto it = m.begin(); it != m.end(); it++) { s << *it << (next(it) == m.end() ? "" : "\n"); } return s; } template ostream& operator<<(ostream& s, unordered_map m) { for (auto it = m.begin(); it != m.end(); it++) { s << *it << (next(it) == m.end() ? "" : "\n"); } return s; } #ifdef _MY_DEBUG #define dump(...) cerr << "/* " << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << endl, dump_func(__VA_ARGS__), cerr << "*/\n\n"; #else #define dump(...) #define endl "\n" #endif void dump_func() { cerr << endl; } template void dump_func(Head&& h, Tail&&... t) { cerr << h << (sizeof...(Tail) == 0 ? "" : ", "), dump_func(forward(t)...); } struct Fast { Fast() { cin.tie(0); ios::sync_with_stdio(false); } } fast; mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count()); constexpr int MOD = 998244353; // *************** TEMPLATE END *************** template T pow(T x, int n, const T UNION = 1) { T ret = UNION; while (n) { if (n & 1) ret *= x; x *= x; n >>= 1; } return ret; } template struct ModInt { int x; static unordered_map to_inv; ModInt() : x(0) {} ModInt(int x_) { if ((x = x_ % MD + MD) >= MD) x -= MD; } ModInt& operator+=(ModInt that) { if ((x += that.x) >= MD) x -= MD; return *this; } ModInt& operator*=(ModInt that) { x = (unsigned long long)x * that.x % MD; return *this; } ModInt& operator-=(ModInt that) { if ((x -= that.x) < 0) x += MD; return *this; } ModInt& operator/=(ModInt that) { x = (unsigned long long)x * that.inv().x % MD; return *this; } ModInt operator-() const { return -x < 0 ? MD - x : -x; } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } bool operator==(ModInt that) const { return x == that.x; } bool operator!=(ModInt that) const { return x != that.x; } ModInt inv() const { return to_inv.count(this->x) ? to_inv[this->x] : (to_inv[this->x] = pow(*this, MD - 2).x); } friend ostream& operator<<(ostream& s, ModInt a) { s << a.x; return s; } friend istream& operator>>(istream& s, ModInt& a) { s >> a.x; return s; } }; template unordered_map ModInt::to_inv; using mint = ModInt; vector fact, fact_inv; void init_factorial(int n) { fact = vector(n + 1, 1); fact_inv = vector(n + 1); for (int i = 0; i < n; i++) fact[i + 1] = fact[i] * (i + 1); fact_inv[n] = mint(1) / fact[n]; for (int i = n - 1; i >= 0; i--) fact_inv[i] = fact_inv[i + 1] * (i + 1); // for (int i = 0; i < n + 1; i++) assert(fact[i] * fact_inv[i] == 1); } mint comb(int n, int r) { return fact[n] * fact_inv[r] * fact_inv[n - r]; } template struct Matrix { vector> A; Matrix() {} Matrix(int n) : A(n, vector< T >(n, 0)) {} Matrix(const vector>& A) : A(A) {} static Matrix I(int n) { Matrix mat(n); for(int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } int height() const { return (A.size()); } int width() const { return (A[0].size()); } vector& operator[](int k) { return A[k]; } const vector& operator[](int k) const { return (A[k]); } Matrix& operator+=(const Matrix &B) { assert(A.size() == B.A.size() && A[0].size() == B.A[0].size()); for(int i = 0; i < A.size(); i++) for(int j = 0; j < A[0].size(); j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { assert(A.size() == B.A.size() && A[0].size() == B.A[0].size()); for(int i = 0; i < A.size(); i++) for(int j = 0; j < A[0].size(); j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { int n = height(), m = B.width(), p = width(); assert(p == B.height()); vector> C(n, vector(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+(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); } vector operator*(const vector& x) const { int n = height(), m = width(); assert(m == x.size()); vector ret(n); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) ret[i] += (*this)[i][j] * x[j]; return ret; } friend ostream &operator<<(ostream &os, Matrix &p) { int 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); } }; signed main() { int n, K; cin >> n >> K; auto make = [&](int a, int b, int c) { a %= K; b %= K; c %= K; return a * K * K + b * K + c; }; Matrix A(K * K * K); REP (a, K) { REP (b, K) { REP (c, K) { A[make(a + 1, b, c)][make(a, b, c)] += 1; A[make(a, b + a, c)][make(a, b, c)] += 1; A[make(a, b, c + b)][make(a, b, c)] += 1; } } } vector x(K * K * K); x[make(0, 0, 0)] = 1; auto res = pow(A, n, Matrix::I(K * K * K)) * x; mint ans = 0; REP (a, K) { REP (b, K) { ans += res[make(a, b, 0)]; } } cout << ans << endl; }