#include using namespace std; #define rep(i, n) for(int i = 0; i < n; i++) #define rep2(i, x, n) for(int i = x; i <= n; i++) #define rep3(i, x, n) for(int i = x; i >= n; i--) #define each(e, v) for(auto &e: v) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; //const int MOD = 1000000007; const int MOD = 998244353; const int inf = (1<<30)-1; const ll INF = (1LL<<60)-1; template bool chmax(T &x, const T &y) {return (x < y)? (x = y, true) : false;}; template bool chmin(T &x, const T &y) {return (x > y)? (x = y, true) : false;}; struct io_setup{ io_setup(){ ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; template struct Mod_Int{ int x; Mod_Int() : x(0) {} Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} Mod_Int &operator += (const Mod_Int &p){ if((x += p.x) >= mod) x -= mod; return *this; } Mod_Int &operator -= (const Mod_Int &p){ if((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int &operator *= (const Mod_Int &p){ x = (int) (1LL * x * p.x % mod); return *this; } Mod_Int &operator /= (const Mod_Int &p){ *this *= p.inverse(); return *this; } Mod_Int &operator ++ () {return *this += Mod_Int(1);} Mod_Int operator ++ (int){ Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator -- () {return *this -= Mod_Int(1);} Mod_Int operator -- (int){ Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator - () const {return Mod_Int(-x);} Mod_Int operator + (const Mod_Int &p) const {return Mod_Int(*this) += p;} Mod_Int operator - (const Mod_Int &p) const {return Mod_Int(*this) -= p;} Mod_Int operator * (const Mod_Int &p) const {return Mod_Int(*this) *= p;} Mod_Int operator / (const Mod_Int &p) const {return Mod_Int(*this) /= p;} bool operator == (const Mod_Int &p) const {return x == p.x;} bool operator != (const Mod_Int &p) const {return x != p.x;} Mod_Int inverse() const{ assert(*this != Mod_Int(0)); return pow(mod-2); } Mod_Int pow(long long k) const{ Mod_Int now = *this, ret = 1; for(; k > 0; k >>= 1, now *= now){ if(k&1) ret *= now; } return ret; } friend ostream &operator << (ostream &os, const Mod_Int &p){ return os << p.x; } friend istream &operator >> (istream &is, Mod_Int &p){ long long a; is >> a; p = Mod_Int(a); return is; } }; using mint = Mod_Int; template struct Matrix{ vector> A; Matrix(int m, int n) : A(m, vector(n, 0)) {} int height() const {return A.size();} int width() const {return A.front().size();} inline const vector &operator [] (int k) const {return A[k];} inline vector &operator [] (int k) {return A[k];} static Matrix I(int l){ Matrix ret(l, l); for(int i = 0; i < l; i++) ret[i][i] = 1; return ret; } Matrix &operator *= (const Matrix &B){ int m = height(), n = width(), p = B.width(); assert(n == B.height()); Matrix ret(m, p); for(int i = 0; i < m; i++){ for(int k = 0; k < n; k++){ for(int j = 0; j < p; j++){ ret[i][j] += A[i][k]*B[k][j]; } } } swap(A, ret.A); return *this; } Matrix operator * (const Matrix &B) const {return Matrix(*this) *= B;} Matrix pow(long long k) const{ int m = height(), n = width(); assert(m == n); Matrix now = *this, ret = I(n); for(; k > 0; k >>= 1, now *= now){ if(k&1) ret *= now; } return ret; } bool eq(const T &a, const T &b) const{ return a == b; //return abs(a-b) <= EPS; } pair row_reduction(vector &b){ //行基本変形を用いて簡約化を行い、(階数、行列式)の組を返す int m = height(), n = width(), check = 0, rank = 0; T det = 1; assert(b.size() == m); for(int j = 0; j < n; j++){ int pivot = check; for(int i = check; i < m; i++){ if(A[i][j] != 0) pivot = i; //if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; //Tが小数の場合はこちら } if(check != pivot) det *= T(-1); swap(A[check], A[pivot]), swap(b[check], b[pivot]); if(eq(A[check][j], T(0))) {det = T(0); continue;} rank++; det *= A[check][j]; for(int k = j+1; k < n; k++) A[check][k] /= A[check][j]; b[check] /= A[check][j]; A[check][j] = T(1); for(int i = 0; i < m; i++){ if(i == check) continue; for(int k = j+1; k < n; k++) A[i][k] -= A[i][j]*A[check][k]; b[i] -= A[i][j]*b[check]; A[i][j] = T(0); } if(++check == m) break; } return make_pair(rank, det); } pair row_reduction(){ vector b(height(), T(0)); return row_reduction(b); } vector> Gausiann_elimination(vector b){ //Ax=bの解の1つと解空間の基底の組を返す int m = height(), n = width(); row_reduction(b); vector> ret; vector p(m, n); vector is_zero(n, true); for(int i = 0; i < m; i++){ for(int j = 0; j < n; j++){ if(!eq(A[i][j], T(0))) {p[i] = j; break;} } if(p[i] < n) is_zero[p[i]] = false; else if(!eq(b[i], T(0))) return {}; } vector x(n, T(0)); for(int i = 0; i < m; i++){ if(p[i] < n) x[p[i]] = b[i]; } ret.push_back(x); for(int j = 0; j < n; j++){ if(!is_zero[j]) continue; x[j] = T(1); for(int i = 0; i < m; i++){ if(p[i] < n) x[p[i]] = -A[i][j]; } ret.push_back(x), x[j] = T(0); } return ret; } }; int K; bool judge(int i, int j, int k){ if(i == K) return true; if(i == j || j == k || k == i) return false; return (i > j && j < k) || (i < j && j > k); } int main(){ int N; cin >> N >> K; int M = (K+1)*(K+1); using mat = Matrix; mat A(2*M, 2*M); rep(i, K+1){ rep(j, K+1){ rep(k, K){ if(!judge(i, j, k)) continue; A[(K+1)*j+k][(K+1)*i+j] += 1; A[M+(K+1)*j+k][M+(K+1)*i+j] += 1; A[M+(K+1)*j+k][(K+1)*i+j] += k; } } } mat x(2*M, 1); x[M-1][0] = 1; A = A.pow(N), A *= x; mint ans1 = 0, ans2 = 0; rep(i, M){ ans1 += A[i][0], ans2 += A[M+i][0]; } cout << ans1 << ' ' << ans2 << '\n'; }