#include <iostream> #include <vector> #include <cstdio> #include <sstream> #include <map> #include <string> #include <algorithm> #include <queue> #include <cmath> #include <functional> #include <set> #include <ctime> #include <random> #include <chrono> #include <cassert> #include <tuple> #include <utility> using namespace std; namespace { using Integer = long long; //__int128; template<class T, class S> istream& operator >> (istream& is, pair<T,S>& p){return is >> p.first >> p.second;} template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;} template<class T> istream& operator , (istream& is, T& val){ return is >> val;} template<class T, class S> ostream& operator << (ostream& os, const pair<T,S>& p){return os << p.first << " " << p.second;} template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(size_t i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;} template<class T> ostream& operator , (ostream& os, const T& val){ return os << " " << val;} template<class H> void print(const H& head){ cout << head; } template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); } template<class ... T> void println(const T& ... values){ print(values...); cout << endl; } template<class H> void eprint(const H& head){ cerr << head; } template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); } template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; } class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator end(){ return range_iterator( end_, step_); } }; inline string operator "" _s (const char* str, size_t size){ return move(string(str)); } constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);} constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);} constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); } inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count()); template<class T> string join(const vector<T>& v, const string& sep){ stringstream ss; for(size_t i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str(); } inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; } } constexpr long long mod = 9_ten + 7; //[n*p] * [p*m] => [n*m] template<class T> vector< vector<T> > multmat(const vector<vector<T> > &A, const vector<vector<T>> &B, int n, int p, int m){ vector<vector<T> > C(n, vector<T>(m,0)); for(int i=0; i<n; i++){ for(int k=0; k<p; k++){ for(int j=0; j<m; j++){ C[i][j] += A[i][k] * B[k][j]; C[i][j] %= mod; } } } return C; } //A[n*n]^k template<class T> vector< vector<T> > mat_pow(vector<vector<T> > A, long long k){ int n = A.size(); vector<vector<T> > ret(n, vector<T>(n, 0) ); for(int i=0; i<n; i++){ ret[i][i] = 1; } while(k>0){ if(k&1) ret = multmat(A,ret, n,n,n); A = multmat(A,A, n,n,n); k>>=1; } return ret; } long long F(long long i){ if(i==0) return 0; if(i==1) return 1; vector<vector<long long>> M={ {1,1}, {1,0} }; auto A = mat_pow(M, i); vector<vector<long long>> x={ {1}, {0} }; auto ans = multmat(A, x, 2,2,1); return ans[1][0]; } long long L(long long i){ if(i==0) return 2; if(i==1) return 1; vector<vector<long long>> M={ {1,1}, {1,0} }; auto A = mat_pow(M, i); vector<vector<long long>> x={ {1}, {2} }; auto ans = multmat(A, x, 2,2,1); return ans[1][0]; } long long G(long long n, long long k){ long long res = F(k*n+k) - my_pow_mod(mod-1,k,mod)*F(k*n)%mod - F(k) + 3*mod; res %= mod; long long inv = L(k) - my_pow_mod(mod-1, k, mod) + mod -1 + mod; inv = my_pow_mod(inv%mod, mod-2, mod); return res*inv%mod; } int main(){ long long n,m; cin >> n,m; for(int i=0; i<10; i++){ eprint(F(i), ""); }eprintln(""); for(int i=0; i<10; i++){ eprint(L(i), ""); }eprintln(""); // long long inv = my_pow_mod(m-1, mod-2, mod); // eprintln(inv); // println( (F(m*n + m-1) - 1 + mod) % mod * inv % mod ); println(G(n,m)); return 0; }