#include using namespace std; #define all(a) a.begin(),a.end() #define pb push_back #define sz(a) ((int)a.size()) using ll=long long; using u32=unsigned int; using u64=unsigned long long; using i128=__int128; using u128=unsigned __int128; using f128=__float128; using pii=pair; using pll=pair; template using vc=vector; template using vvc=vc>; template using vvvc=vc>; using vi=vc; using vll=vc; using vvi=vc; using vvll=vc; #define vv(type,name,n,...) \ vector> name(n,vector(__VA_ARGS__)) #define vvv(type,name,n,m,...) \ vector>> name(n,vector>(m,vector(__VA_ARGS__))) template using min_heap=priority_queue,greater>; template using max_heap=priority_queue; // https://trap.jp/post/1224/ #define rep1(n) for(ll i=0; i<(ll)(n); ++i) #define rep2(i,n) for(ll i=0; i<(ll)(n); ++i) #define rep3(i,a,b) for(ll i=(ll)(a); i<(ll)(b); ++i) #define rep4(i,a,b,c) for(ll i=(ll)(a); i<(ll)(b); i+=(c)) #define cut4(a,b,c,d,e,...) e #define rep(...) cut4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__) #define per1(n) for(ll i=((ll)n)-1; i>=0; --i) #define per2(i,n) for(ll i=((ll)n)-1; i>=0; --i) #define per3(i,a,b) for(ll i=((ll)a)-1; i>=(ll)(b); --i) #define per4(i,a,b,c) for(ll i=((ll)a)-1; i>=(ll)(b); i-=(c)) #define per(...) cut4(__VA_ARGS__,per4,per3,per2,per1)(__VA_ARGS__) #define rep_subset(i,s) for(ll i=(s); i>=0; i=(i==0?-1:(i-1)&(s))) template constexpr T ifloor(const T a, const S b){return a/b-(a%b&&(a^b)<0);} template constexpr T iceil(const T a, const S b){return ifloor(a+b-1,b);} template void sort_unique(vector &vec){ sort(vec.begin(),vec.end()); vec.resize(unique(vec.begin(),vec.end())-vec.begin()); } template constexpr bool chmin(T &a, const S b){if(a>b) return a=b,true; return false;} template constexpr bool chmax(T &a, const S b){if(a istream& operator >> (istream& i, pair &p){return i >> p.first >> p.second;} template ostream& operator << (ostream& o, const pair &p){return o << p.first << ' ' << p.second;} #ifdef i_am_noob #define bug(...) cerr << "#" << __LINE__ << ' ' << #__VA_ARGS__ << "- ", _do(__VA_ARGS__) template void _do(vector x){for(auto i: x) cerr << i << ' ';cerr << "\n";} template void _do(set x){for(auto i: x) cerr << i << ' ';cerr << "\n";} template void _do(unordered_set x){for(auto i: x) cerr << i << ' ';cerr << "\n";} template void _do(T && x) {cerr << x << endl;} template void _do(T && x, S&&...y) {cerr << x << ", "; _do(y...);} #else #define bug(...) 777771449 #endif template void print(vector x){for(auto i: x) cout << i << ' ';cout << "\n";} template void print(set x){for(auto i: x) cout << i << ' ';cout << "\n";} template void print(unordered_set x){for(auto i: x) cout << i << ' ';cout << "\n";} template void print(T && x) {cout << x << "\n";} template void print(T && x, S&&... y) {cout << x << ' ';print(y...);} template istream& operator >> (istream& i, vector &vec){for(auto &x: vec) i >> x; return i;} vvi read_graph(int n, int m, int base=1){ vvi adj(n); for(int i=0,u,v; i> u >> v,u-=base,v-=base; adj[u].pb(v),adj[v].pb(u); } return adj; } vvi read_tree(int n, int base=1){return read_graph(n,n-1,base);} template pair operator + (const pair &a, const pair &b){return {a.first+b.first,a.second+b.second};} template constexpr T inf=0; template<> constexpr int inf = 0x3f3f3f3f; template<> constexpr ll inf = 0x3f3f3f3f3f3f3f3f; template vector operator += (vector &a, int val){for(auto &i: a) i+=val; return a;} template T isqrt(const T &x){T y=sqrt(x+2); while(y*y>x) y--; return y;} #define ykh mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()) #include using namespace atcoder; using mint=modint998244353; //using mint=modint1000000007; struct num{ mint a,b; num(){a=b=0;} num(mint x){a=x,b=0;} num(mint x, mint y){a=x,b=y;} num operator + (num o){ return {a+o.a,b+o.b}; } num operator += (num o){ return (*this)=(*this)+o; } num operator - (num o){ return {a-o.a,b-o.b}; } num operator * (num o){ return {a*o.a+b*o.b*5,a*o.b+b*o.a}; } num pow(ll m){ num res(1); num cur=*this; for(; m; m>>=1,cur=cur*cur) if(m&1) res=res*cur; return res; } }; template struct matrix: array,N>{ matrix(){for(int i=0; i vec){ for(int i=0; i=0); matrix res=id(),cur=*this; for(; x; cur=cur*cur,x>>=1) if(x&1) res=res*cur; return res; } }; template ostream& operator << (ostream& o, matrix x){ for(int i=0; i vector> calc_nCr(int n){ vector> res; for(int i=0; i(i+1)); for(int j=0; j<=i; ++j){ if(j==0||j==i) res[i][j]=1; else res[i][j]=res[i-1][j-1]+res[i-1][j]; } } return res; } void ahcorz(){ ll n; int k; cin >> n >> k; auto C=calc_nCr(k+2); num x(mint(2).inv(),mint(2).inv()),y(mint(2).inv(),-mint(2).inv()); num res; rep(k+1){ matrix mat; mat[1][0]=mat[1][1]=num(1); mat[0][0]=x.pow(i)*y.pow(k-i); mat=mat^(n+1); res+=mat[1][0]*num(C[k][i])*num((k-i)&1?-1:1); } res=res*(num(0,mint(5).inv()).pow(k)); print(res.a.val()); //print(res.b.val()); } signed main(){ ios_base::sync_with_stdio(0),cin.tie(0); cout << fixed << setprecision(20); int t=1; //cin >> t; while(t--) ahcorz(); }