#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;} #include using namespace std; template T interpolation(vector&X,vector&Y,T x){ assert(X.size()==Y.size()); int N=X.size(); T ans=0; rep(i,0,N){ T a=Y[i]; rep(j,0,N)if(i!=j)a*=x-X[j],a/=X[i]-X[j]; ans+=a; } return ans; } vm inv(const vm&f){ vm g{1/f[0]}; while(sz(g) pair,vector>div(vectorf,const vector&g){ if(f.size()(0),f); reverse(f.begin(),f.end()); vectorh=g; reverse(h.begin(),h.end()); while(h.size()+g.size()<=f.size())h.emplace_back(0); vectorq=convolution(f,inv(h)); q.resize(f.size()-g.size()+1); reverse(q.begin(),q.end()); auto r=convolution(g,q); reverse(f.begin(),f.end()); for(int i=0;isync_with_stdio(0); cin.exceptions(cin.failbit); ll K,L,R;cin>>K>>L>>R; vm B(K+10); rep(i,1,K+10)B[i]=B[i-1]+pow_mod(i,K,mod); vm A(K+10); iota(all(A),0); vm C(K+10); rep(i,0,K+10)C[i]=pow_mod(i,K,mod); rep(_,0,K+1)rrep(i,1,K+10)C[i]-=C[i-1]; vm D(K+3); D[0]=1; rep(_,0,K+1)rrep(i,0,_+1)D[i+1]-=D[i]; rrep(i,0,K+2)D[i+1]-=K*D[i]; vm g(K+3,1); rep(i,0,K+3)g[i]=D[K+2-i]; auto ID=inv(D); vvm T(60); T[0]=vm{0,1}; rep(i,1,60)T[i]=div(convolution(T[i-1],T[i-1]),g).second; auto eval=[&](ll N)->mint{ vm rd=vm{1}; rep(i,0,60)if((N>>i)%2)rd=div(convolution(rd,T[i]),g).second; mint ans=0; rep(i,0,sz(rd))ans+=ID[i]*rd[i]; return ans; }; auto f=[&](ll N)->mint{ if(N<0)return 0; mint ans=0; if(N>1){ mint n=N; if(K==1)ans=(n+1)*n*(n-1)/6; else{ mint r=inv_mod(K-1,mod),s=0; rep(i,0,sz(C))if(N-1-i>=0)s+=C[i]*eval(N-1-i); ans=r*(K*s-interpolation(A,B,mint(N-1))); } } if(K==1)ans+=(N%mod+2)*(N%mod+1)%mod*((mod+1)/2); else{ mint r=inv_mod(1-K,mod); ans+=(1-pow_mod(K,N,mod)*(K+N%mod)+(1-pow_mod(K,N,mod))*r)*r; } return ans; }; cout<