#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint998244353; mint f[120]; mint fact[120], ifact[120]; mint comb(int n, int k) { return fact[n] * ifact[k] * ifact[n - k]; } template struct Mat : array, N> { using M = Mat; void make_identity() { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { (*this)[i][j] = zero(); } } for (int i = 0; i < N; i++) { (*this)[i][i] = one(); } } M& operator+=(const M& rhs) { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { (*this)[i][j] = add((*this)[i][j], rhs[i][j]); } } return *this; } M& operator*=(const M& rhs) { static M temp; for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { temp[i][j] = zero(); } } for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { for (int k = 0; k < N; k++) { temp[i][k] = add(temp[i][k], mul((*this)[i][j], rhs[j][k])); } } } *this = temp; return *this; } template void inplace_pow(I k) { assert(k >= 0); static M temp; temp = *this; make_identity(); while (k) { if (k & 1) *this *= temp; k >>= 1; if (k) temp *= temp; } } friend ostream& operator<<(ostream& os, const M& A) { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { os << A[i][j] << " \n"[j + 1 == N]; } } return os; } }; // mint mint add(mint x, mint y) { return x + y; } mint zero() { return mint(); } mint mul(mint x, mint y) { return x * y; } mint one() { return mint::raw(1); } using M = Mat; } int main() { ios::sync_with_stdio(false); cin.tie(0); f[1] = 1; rep(i, 110) f[i+2] += f[i], f[i+1] += f[i]; fact[0] = 1; for (int i = 1; i < 110; i++) fact[i] = fact[i-1] * f[i]; ifact[109] = fact[109].inv(); rrep(i, 109) ifact[i] = ifact[i+1] * f[i+1]; // int k; // cin >> k; // vector dp(100), naive(100); // rep(i, 100) naive[i] = f[i].pow(k); // rep(i, 30) cout << naive[i].val() << ' '; // cout << endl; // for (int i = k + 1; i < 30; i++) { // mint v; // for (int j = 1; j <= k + 1; j++) { // mint add = naive[i - j] * comb(k + 1, j); // if ((j - 1) / 2 % 2 == 0) v += add; // else v -= add; // } // cout << v.val() << ' ' << naive[i].val() << endl; // } ll n; int k; cin >> n >> k; M a; a[0][101] = 1; a[101][101] = 1; for (int i = 1; i <= k; i++) a[i][i-1] = 1; for (int j = 1; j <= k + 1; j++) { mint add = comb(k + 1, j); if ((j - 1) / 2 % 2) add = -add; a[k+1-j][k] = add; // cout << k + 1 - j << ' ' << k << ' ' << add.val() << endl; } a.inplace_pow(n + 1); mint ans; rep(i, k + 1) ans += f[i].pow(k) * a[i][101]; // vector nvec(k + 1); // rep(i, k + 1) rep(j, k + 1) nvec[j] = f[i] * a[i][j]; // rep(i, k +1) cout << nvec[i].val() << " \n"[i + 1 == k +1]; cout << ans.val() << '\n'; }