#include<bits/stdc++.h> using namespace std; typedef long long ll; typedef unsigned long long ull; #define rep(i,a,n) for(ll i=a;i<n;i++) #define per(i,a,n) for(ll i=n-1;i>=a;i--) #define pb push_back #define mp make_pair #define all(x) (x).begin(),(x).end() #define fi first #define se second #define SZ(x) (ll)(x).size() typedef vector<ll>VI; typedef pair<ll,ll>PII; const int mod=1e9+7; ll powmod(ll a,ll b){ ll res=1; a%=mod; assert(b>=0); for(;b;b>>=1){ if(b&1)res=res*a%mod; a=a*a%mod; }return res; } ll _,n; namespace gauss{ const ll N=10010; ll res[N],base[N],_c[N],_md[N]; vector<ll>Md; void mul(ll *a,ll *b,ll k){ rep(i,0,k+k)_c[i]=0; rep(i,0,k)if(a[i])rep(j,0,k) _c[i+j]=(_c[i+j]+a[i]*b[j])%mod; for(ll i=k+k-1;i>=k;i--) if(_c[i]) rep(j,0,SZ(Md)) _c[i-k+Md[j]]=(_c[i-k+Md[j]]-_c[i]*_md[Md[j]])%mod; rep(i,0,k)a[i]=_c[i]; } ll solve(ll n,VI a,VI b){ ll ans=0,pnt=0; ll k=SZ(a); assert(SZ(a)==SZ(b)); rep(i,0,k)_md[k-1-i]=-a[i];_md[k]=1; Md.clear(); rep(i,0,k)if(_md[i]!=0)Md.pb(i); rep(i,0,k)res[i]=base[i]=0; res[0]=1; while((1ll<<pnt)<=n)pnt++; for(ll p=pnt;p>=0;p--){ mul(res,res,k); if((n>>p)&1){ for(ll i=k-1;i>=0;i--)res[i+1]=res[i];res[0]=0; rep(j,0,SZ(Md))res[Md[j]]=(res[Md[j]]-res[k]*_md[Md[j]])%mod; } } rep(i,0,k)ans=(ans+res[i]*b[i])%mod; if(ans<0)ans+=mod; return ans; } VI BM(VI s){ VI C(1,1),B(1,1); ll L=0,m=1,b=1; rep(n,0,SZ(s)){ ll d=0; rep(i,0,L+1)d=(d+1ll*C[i]*s[n-i])%mod; if(d==0)++m; else if(2*L<=n){ VI T=C; ll c=mod-d*powmod(b,mod-2)%mod; while(SZ(C)<SZ(B)+m)C.pb(0); rep(i,0,SZ(B))C[i+m]=(C[i+m]+c*B[i])%mod; L=n+1-L;B=T;b=d;m=1; } else { ll c=mod-d*powmod(b,mod-2)%mod; while(SZ(C)<SZ(B)+m)C.pb(0); rep(i,0,SZ(B))C[i+m]=(C[i+m]+c*B[i])%mod; ++m; } }return C; } ll gao(VI a,ll n){ VI c=BM(a); c.erase(c.begin()); rep(i,0,SZ(c))c[i]=(mod-c[i])%mod; return solve(n,c,VI(a.begin(),a.begin()+SZ(c))); } }; VI g; ll f[1100]; ll sum[1100]; int main() { ll n,k; f[1]=1; f[2]=2; cin>>n>>k; for(int i=3;i<=200;i++)f[i]=(f[i-1]+f[i-2])%mod; g.clear(); sum[0]=0; for(int i=1;i<=200;i++){ sum[i]=(f[i]*powmod(i,k)+sum[i-1])%mod; g.pb(sum[i]); } printf("%lld\n",gauss::gao(g,n-1)); }
BM
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