#include #include using namespace std; using namespace atcoder; typedef long long int ll; typedef long double ld; typedef vector vi; typedef vector vl; typedef vector vvl; typedef vector vvvl; typedef vector vvvvl; typedef vector vb; typedef vector vvb; typedef vector vvvb; typedef vector vvvvb; typedef pair pl; typedef pair ppl; typedef pair pppl; typedef pair pppppl; #define rep(i,a,b) for(int i=(a);i<(b);i++) #define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--) #define all(a) begin(a),end(a) #define sz(a) (int)(a).size() #define F first #define S second #define bs(A,x) binary_search(all(A),x) #define lb(A,x) (ll)(lower_bound(all(A),x)-A.begin()) #define ub(A,x) (ll)(upper_bound(all(A),x)-A.begin()) #define cou(A,x) (ll)upper_bound(all(A),x)-lower_bound(all(A),x)) templateusing min_priority_queue=priority_queue,greater>; templatebool chmax(T&a,T b){if(abool chmin(T&a,T b){if(b vm; typedef vector vvm; typedef vector vvvm; typedef vector vvvvm; ostream&operator<<(ostream&os,mint a){os<>(istream&is,mint&a){int x;is>>x;a=mint(x);return is;} //*/ templateostream&operator<<(ostream&os,pairp){os<istream&operator>>(istream&is,pair&p){is>>p.F>>p.S;return is;} templateostream&operator<<(ostream&os,vectorv){rep(i,0,sz(v))os<istream&operator>>(istream&is,vector&v){for(T&in:v)is>>in;return is;} vm inv(const vm&f){ vm g{1/f[0]}; while(sz(g)sync_with_stdio(0); cin.exceptions(cin.failbit); ll N,K;cin>>N>>K; N+=K; vm a(2*K+2,1); rep(n,K+1,2*K+2)a[n]=a[n-1]-a[n-K-1]+pow_mod(2,n-K-1,mod); ll d=2*K+2; vm F(d+1); F[0]+=1; F[K]+=-2; F[K+1]+=1; F[2*K]+=2; F[2*K+1]+=-3; F[d]+=1; reverse(all(F)); auto invF=inv(F); reverse(all(F)); vvm G(40); G[0]=vm{0,1}; auto rem=[&](vm&f){ if(sz(f)<=d)return; reverse(all(f)); assert(f[0].val()); auto q=convolution(f,invF); q.resize(sz(f)-sz(F)+1); reverse(all(q)); q=convolution(q,F); reverse(all(f)); f.resize(d); rep(i,0,d)f[i]-=q[i]; }; vm ans={1},T={0,1}; while(N){ if(N%2){ans=convolution(ans,T);rem(ans);} T=convolution(T,T);rem(T);N/=2; } mint s=0; rep(i,0,d)s+=ans[i]*a[i]; cout<