#ifdef LOCAL111 #define _GLIBCXX_DEBUG #else #define NDEBUG #endif #define _USE_MATH_DEFINES #include const int INF = 1e9; using namespace std; template ostream& operator<< (ostream& os, const pair& p) { os << '(' << p.first << ' ' << p.second << ')'; return os; } #define endl '\n' #define ALL(a) (a).begin(),(a).end() #define SZ(a) int((a).size()) #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--) #define REP(i,n) FOR(i,0,n) #define RREP(i,n) for (int i=(n)-1;i>=0;i--) #ifdef LOCAL111 #define DEBUG(x) cout<<#x<<": "<<(x)< void dpite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;} #else #define DEBUG(x) true template void dpite(T a, T b){ return; } #endif #define F first #define S second #define SNP string::npos #define WRC(hoge) cout << "Case #" << (hoge)+1 << ": " template void pite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;} template bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;} template bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;} typedef long long int LL; typedef unsigned long long ULL; typedef pair P; void ios_init(){ //cout.setf(ios::fixed); //cout.precision(12); #ifdef LOCAL111 return; #endif ios::sync_with_stdio(false); cin.tie(0); } template class ModInt { public: const static long long mod = MOD; long long x; ModInt() { x = 0; } ModInt(long long x) { x %= mod; this->x = x < 0 ? x+mod : x; } int get() const { return (int)x; } ModInt &operator+=(ModInt that) { if((x += that.get()) >= mod) x -= mod; return *this; } ModInt &operator-=(ModInt that) { if((x += mod-that.get()) >= mod) x -= mod; return *this; } ModInt &operator*=(ModInt that) { x = x*that.get()%mod; return *this; } ModInt &operator/=(ModInt that) { return *this *= that.inverse(); } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt inverse() const { using std::swap; long long a = x, b = mod, u = 1, v = 0; while(b) { long long t = a/b; a -= t*b; swap(a,b); u -= t*v; swap(u,v); } return ModInt(u); } ModInt pow(int n) const{ ModInt b = *this; ModInt res = 1; while(n != 0) { if(n&1){ res *= b; } b *= b; n >>= 1; } return res; } bool operator==(ModInt that) const { return x == that.get(); } bool operator!=(ModInt that) const { return x != that.get(); } ModInt operator-() const { return x == 0 ? 0 : ModInt(mod-x); } }; template ostream& operator<< (ostream& os, const ModInt& m) { os << m.get(); return os; } template istream& operator>> (istream& is, ModInt& m){ long long n; is >> n; m = n; return is;} typedef ModInt<1000000007> mint; #define EPS 1e-9 //library template class Matrix { public: vector > v; int n,m; Matrix(int n){ this->n = this->m = n; v.resize(n,vector(n,0)); } Matrix(int n, int m){ this -> n = n; this -> m = m; v.resize(n,vector(m,0)); } size_t size() const { return v.size(); } int row() const { return n; } int col() const { return m; } Matrix operator+ (Matrix x) const { Matrix res(n,m); for(int i = 0; i < n; i++){ for(int j = 0; j < m; j++){ res.v[i][j] = x.v[i][j]+v[i][j]; } } return res; } Matrix operator-(Matrix x) const { Matrix res(n,m); for(int i = 0; i < n; i++){ for(int j = 0; j < m; j++){ res.v[i][j] = v[i][j]-x.v[i][j]; } } } Matrix operator*(Matrix x) const { Matrix res(n,x.m); for(int i = 0; i < n; i++){ for(int j = 0; j < x.m; j++){ for(int k = 0; k < m; k++){ res.v[i][j] += v[i][k]*x.v[k][j]; } } } return res; } Matrix operator-() const { Matrix res = *this; for(int i = 0; i < (int)v.size(); ++i) { for(int j = 0; j < (int)v[i].size(); ++j) { res [i][j] *= -1; } } return res; } vector operator*(vector x) const { assert(x.size() == v.size()); vector res(v.size()); for(int i = 0; i < n; i++){ T tmp = 0; for(int j = 0; j < m; j++){ tmp += v[i][j]*x[j]; } res[i] = tmp; } return res; } Matrix pow(long long x) const { assert(n == m); Matrix m = (*this); Matrix res(n); for(int i = 0; i < n; i++) res[i][i] = 1; while(x != 0) { if(x&1) { res = res*m; } m = m*m; x >>= 1; } return res; } vector& operator[](int x){ return v[x]; } const vector& operator[](int x) const { return v[x]; } Matrix inverse() const{ assert(n == m); Matrix res(n); for(int i = 0; i < n; ++i) { res[i][i] = 1; } // vector> swap_log; Matrix mat = *this; for(int k = 0; k < n; ++k) { T max_val = abs(mat[k][k]); int max_point = k; for(int i = k+1; i < n; ++i) { if(max_val < abs(mat[i][k])){ max_val = abs(mat[i][k]); max_point = i; } } swap(mat[k],mat[max_point]); swap(res[k],res[max_point]); // swap_log.emplace_back(k,max_point); for(int i = k+1; i < n; ++i) { T m = mat[i][k]/mat[k][k]; for(int j = 0; j < n; ++j) { mat[i][j] -= m*mat[k][j]; res[i][j] -= m*res[k][j]; } } } for(int k = n-1; k >= 0; --k) { for(int i = 0; i < k; ++i) { T m = mat[i][k]/mat[k][k]; for(int j = 0; j < n; ++j) { // mat[i][j] -= mat[k][j]*m; res[i][j] -= res[k][j]*m; } } } for(int i = 0; i < n; ++i) { for(int j = 0; j < n; ++j) { res[i][j] /= mat[i][i]; } } // for(auto&& e : swap_log) { // swap(res[e.first],res[e.second]); // } return res; } T det() const { Matrix mat = *this; T res = 1; for(int k = 0; k < n; ++k) { T max_val = abs(mat[k][k]); int max_point = k; for(int i = k+1; i < n; ++i) { if(max_val < abs(mat[i][k])){ max_val = abs(mat[i][k]); max_point = i; } } swap(mat[k],mat[max_point]); if(k != max_point) res *= -1; for(int i = k+1; i < n; ++i) { T m = mat[i][k]/mat[k][k]; for(int j = 0; j < n; ++j) { mat[i][j] -= m*mat[k][j]; } } } for(int i = 0; i < n; ++i) { res *= mat[i][i]; } return res; } }; //libary int main() { ios_init(); LL n, m; while(cin >> n >> m) { Matrix A(3); Matrix B(2); B[0] = {1, 1}; B[1] = {1, 0}; B = B.pow(m); A[0] = {1, 0, 1}; A[1] = {0, 0, 0}; A[2] = {0, 0, 0}; REP(i, 2) REP(j, 2) A[i+1][j+1] = B[i][j]; vector v = {0, 1, 0}; auto ans = A.pow(n+1) * v; cout << ans[0] << endl; } return 0; }