#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #ifdef LOCAL # include "debug_print.hpp" # define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else # define debug(...) (static_cast(0)) #endif using namespace std; #define rep1(a) for(int i = 0; i < a; i++) #define rep2(i, a) for(int i = 0; i < a; i++) #define rep3(i, a, b) for(int i = a; i < b; i++) #define rep4(i, a, b, c) for(int i = a; i < b; i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(a) for(int i = (a)-1; i >= 0; i--) #define rrep2(i, a) for(int i = (a)-1; i >= 0; i--) #define rrep3(i, a, b) for(int i = (b)-1; i >= a; i--) #define rrep4(i, a, b, c) for(int i = (b)-1; i >= a; i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() #define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() ); #define pb push_back using ll = long long; using D = double; using LD = long double; using P = pair; using vi = vector; using vl = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) template using PQ = priority_queue>; template using minPQ = priority_queue, greater>; templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &...u) { cout << t; outr(u...); } template struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % mod) { if (val < 0) val += mod; } constexpr int getmod() { return mod; } constexpr Fp operator - () const noexcept { return val ? mod - val : 0; } constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; } constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; } constexpr Fp& operator += (const Fp& r) noexcept { val += r.val; if (val >= mod) val -= mod; return *this; } constexpr Fp& operator -= (const Fp& r) noexcept { val -= r.val; if (val < 0) val += mod; return *this; } constexpr Fp& operator *= (const Fp& r) noexcept { val = val * r.val % mod; return *this; } constexpr Fp& operator /= (const Fp& r) noexcept { long long a = r.val, b = mod, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } val = val * u % mod; if (val < 0) val += mod; return *this; } constexpr bool operator == (const Fp& r) const noexcept { return this->val == r.val; } constexpr bool operator != (const Fp& r) const noexcept { return this->val != r.val; } friend constexpr ostream& operator << (ostream &os, const Fp& x) noexcept { return os << x.val; } friend constexpr Fp modpow(const Fp &a, long long n) noexcept { if (n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } }; template struct BiCoef { vector fact_, inv_, finv_; constexpr BiCoef() {} constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) { init(n); } constexpr void init(int n) noexcept { fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1); int mod = fact_[0].getmod(); for(int i = 2; i < n; i++){ fact_[i] = fact_[i-1] * i; inv_[i] = -inv_[mod%i] * (mod/i); finv_[i] = finv_[i-1] * inv_[i]; } } constexpr T com(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n-k]; } constexpr T perm(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[n-k]; } constexpr T fact(int n) const noexcept { if (n < 0) return 0; return fact_[n]; } constexpr T inv(int n) const noexcept { if (n < 0) return 0; return inv_[n]; } constexpr T finv(int n) const noexcept { if (n < 0) return 0; return finv_[n]; } }; //const int mod = 1e9+7; const int mod = 998244353; using mint = Fp; BiCoef bc; template struct Matrix{ int r,c; vector> a; Matrix(int r, int c, T init = 0) : r(r), c(c), a(r, vector(c, init)) {} Matrix& unit(){ assert(r == c); rep(i,r) a[i][i] = 1; return *this; } const vector& operator[] (int i) const {return a[i];} vector& operator[] (int i) {return a[i];} Matrix operator* (const Matrix& b) const{ assert(c == b.r); Matrix res(r, b.c); rep(i,r)rep(k,c)rep(j,b.c) res[i][j] += a[i][k] * b[k][j]; return res; } Matrix pow(ll k) const{ assert(r == c); Matrix now = *this; Matrix res = Matrix(r,c).unit(); while(k){ if(k & 1) res = res * now; now = now * now; k >>= 1; } return res; } }; using mat = Matrix; mint p[101], q[101]; int main(){ ios_base::sync_with_stdio(false); cin.tie(nullptr); ll n,k; in(n,k); bc.init(k+1); p[0] = 1; q[0] = 0; const mint inv2 = (mint)1/2; const mint inv5 = (mint)1/5; rep(i,1,k+1){ p[i] = (p[i-1] + q[i-1]*5) * inv2; q[i] = (p[i-1] + q[i-1]) * inv2; } mint ans = 0; rep(i,k+1){ mint p0 = p[k-i], q0 = q[k-i]; mint p1 = p[i], q1 = -q[i]; mint a = p0*p1 + q0*q1*5, b = p0*q1 + p1*q0; mat f(3,3); f[0][0] = f[1][1] = a; f[0][1] = b*5; f[1][0] = b; f[0][2] = f[2][2] = 1; mat v(3,1); v[0][0] = v[2][0] = 1; v = f.pow(n) * v; if(k&1){ ans += modpow(inv5,k/2) * bc.com(k,i) * v[1][0] * (i&1 ? -1:1); } else{ ans += modpow(inv5,k/2) * bc.com(k,i) * v[0][0] * (i&1 ? -1:1); } } out(ans); }