#include using namespace std; #include using mint = atcoder::modint998244353; #define rep(i, l, r) for (int i = (int)(l); i < (int)(r); i++) #define ll long long //行列累乗ライブラリ using mat = vector>; int hei(const mat& a) {return (int)a.size();} int wid(const mat& a) {return (int)a[0].size();} //行列乗算 O(K^3) mat mul(const mat& a, const mat& b) { int ah = hei(a), aw = wid(a), bh = hei(b), bw = wid(b); assert(aw == bh); mat c(ah, vector(bw, 0)); rep(i, 0, ah) rep(j, 0, bw) { rep(k, 0, aw) { c[i][j] += a[i][k] * b[k][j]; } } return c; } //行列累乗 O(K^3 log N) mat pow(mat a, ll p) { assert(hei(a) == wid(a)); int n = hei(a); mat ret(n, vector(n)); rep(i, 0, n) ret[i][i] = 1; while(p > 0) { if (p&1) { ret = mul(a, ret); } a = mul(a, a); p>>=1; } return ret; } //二項係数ライブラリ struct combination { vector fac, infac; combination(int n) { fac.resize(n+1); infac.resize(n+1); fac[0] = 1; for (int i = 1; i <= n; i++) fac[i] = fac[i-1]*i; infac[n] = fac[n].inv(); for (int i = n; i >= 1; i--) infac[i-1] = infac[i]*i; } mint operator()(int n, int k) { if (k > n || k < 0) return 0; return fac[n]*infac[k]*infac[n-k]; } }comb(100); //comb(n, k) で nCk int main() { ll N; int K; cin >> N >> K; //行列累乗用の正方行列 mat M(K+2, vector(K+2, 0)); rep(i, 0, K+1) { int n = K-i; rep(j, 0, K+1) { int k = K-j-i; M[i][j] = comb(n, k); } } //Sに関する部分 M[K+1][0] = M[K+1][K+1] = 1; //行列累乗後 mat Mpow = pow(M, N); //初期値。F_0 = 0 を利用する mat z(K+2, vector(1, 0)); z[0][0] = 1; //答えとなる行列を求める mat ans = mul(Mpow, z); //答えを出力 cout << ans[K+1][0].val() << endl; }