/** * author: nok0 * created: 2020.09.14 11:55:35 **/ #ifdef LOCAL #define _GLIBCXX_DEBUG #endif #include using namespace std; #pragma region Macros #define ll long long #define ld long double #define FOR(i,l,r) for(int i=(l);i<(r);++i) #define REP(i,n) FOR(i,0,n) #define REPS(i,n) FOR(i,1,n+1) #define RFOR(i,l,r) for(int i=(l);i>=(r);--i) #define RREP(i,n) RFOR(i,n-1,0) #define RREPS(i,n) RFOR(i,n,1) #define pb push_back #define eb emplace_back #define SZ(x) ((int)(x).size()) #define all(x) (x).begin(),(x).end() #define rall(x) (x).rbegin(),(x).rend() template using V = vector; template using VV = V>; using pii = pair; using pll = pair; #define VEC(type, name, size)\ V name(size);\ IN(name) #define VVEC(type, name, h, w)\ VV name(h, V(w));\ IN(name) #define INT(...)\ int __VA_ARGS__;\ IN(__VA_ARGS__) #define LL(...)\ ll __VA_ARGS__;\ IN(__VA_ARGS__) #define STR(...)\ string __VA_ARGS__;\ IN(__VA_ARGS__) #define CHAR(...)\ char __VA_ARGS__;\ IN(__VA_ARGS__) #define DOUBLE(...)\ DOUBLE __VA_ARGS__;\ IN(__VA_ARGS__) #define LD(...)\ LD __VA_ARGS__;\ IN(__VA_ARGS__) void scan(int &a) { cin >> a; } void scan(long long &a) { cin >> a; } void scan(char &a) { cin >> a; } void scan(double &a) { cin >> a; } void scan(long double &a) { cin >> a; } void scan(char a[]) { scanf("%s", a); } void scan(string &a) { cin >> a; } template void scan(V &); template void scan(pair &); template void scan(V &a) { for(auto &i : a) scan(i); } template void scan(pair &p){ scan(p.first); scan(p.second); } template void scan(T &a) { cin >> a; } void IN() {} template void IN(Head &head, Tail &... tail) { scan(head); IN(tail...); } template inline void print(T x){ cout << x << '\n';} template istream &operator>>(istream &is, pair &p){ is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const pair &p){ os << p.first << " " << p.second; return os; } template ostream &operator<<(ostream &os, const V &v){ REP(i, SZ(v)){ if(i) os << " "; os << v[i]; } return os; } //debug template void view(const V &v){ cerr << "{ "; for(const auto &e : v){ cerr << e << ", "; } cerr << "\b\b }"; } template void view(const VV &vv){ cerr << "{\n"; for(const auto &v : vv){ cerr << "\t"; view(v); cerr << "\n"; } cerr << "}"; } template void view(const V> &v){ cerr << "{\n"; for(const auto &c : v) cerr << "\t(" << c.first << ", " << c.second << ")\n"; cerr << "}"; } template void view(const map &m){ cerr << "{\n"; for(auto &t : m) cerr << "\t[" << t.first << "] : " << t.second << "\n"; cerr << "}"; } template void view(const pair &p){ cerr << "(" << p.first << ", " << p.second << ")";} template void view(const set &s) { cerr << "{ "; for(auto &t : s) { view(t); cerr << ", "; } cerr << "\b\b }"; } template void view(T e) { cerr << e;} #ifdef LOCAL void debug_out() {} template void debug_out(Head H, Tail... T) { view(H); cerr << ", "; debug_out(T...); } #define debug(...) \ do{ \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \ debug_out(__VA_ARGS__); \ cerr << "\b\b]\n"; \ } while(0) #else #define debug(...) (void(0)) #endif template V press(V &x){ V res = x; sort(all(res)); res.erase(unique(all(res)), res.end()); REP(i, SZ(x)){ x[i] = lower_bound(all(res), x[i]) - res.begin(); } return res; } template inline bool chmin(T& a, T b) {if (a > b) {a = b; return true; }return false; } template inline bool chmax(T& a, T b) {if (a < b) {a = b; return true; }return false; } inline void Yes(bool b = true) {cout << (b ? "Yes" : "No") << '\n';} inline void YES(bool b = true) {cout << (b ? "YES" : "NO") << '\n';} inline void err(bool b = true) {if(b) {cout << -1 << '\n'; exit(0);}} template inline void fin(bool b = true, T e = 0) {if(b) {cout << e << '\n'; exit(0);}} template T divup(T x, T y) {return (x+(y-1))/y;} template T pow(T a, long long n, T e = 1) {T ret = e; while (n) {if (n & 1) ret *= a; a *= a; n >>= 1; } return ret; } struct iofast{iofast(){ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15);}}iofast_; const int inf = 1e9; const ll INF = 1e18; #pragma endregion template struct Matrix{ private: std::vector> A; static Matrix I(size_t n){ Matrix mat(n); for(int i = 0; i < n; i++) mat[i][i] = 1; return mat; } public: Matrix() {} Matrix(std::vector> &vvec){ A = vvec;} Matrix(size_t n, size_t m) : A(n, std::vector(m, 0)) {} Matrix(size_t n, size_t m, T init) : A(n, std::vector(m, init)) {} Matrix(size_t n, std::vector &vec) : A(n, vec) {} Matrix(size_t n) : A(n, std::vector(n, 0)) {} size_t height() const {return A.size();} size_t width() const {return A[0].size();} inline const std::vector &operator[] (int k) const{ return A[k]; } inline std::vector &operator[] (int k){ return A[k]; } Matrix &operator+= (const Matrix &B){ size_t n = height(), m = width(); assert(n == B.height() and m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return *this; } Matrix &operator-= (const Matrix &B){ size_t n = height(), m = width(); assert(n == B.height() and m == B.width()); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return *this; } Matrix &operator*= (const Matrix &B){ size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); std::vector> C(n, std::vector(m, 0)); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) for(int k = 0; k < p; k++) C[i][j] += (*this)[i][k] * B[k][j]; A.swap(C); return *this; } Matrix &operator^= (long long k){ Matrix B = Matrix::I(height()); while(k > 0){ if(k & 1) B *= (*this); *this *= *this; k >>= 1ll; } A.swap(B.A); return *this; } bool operator== (const Matrix &B){ size_t n = height(), m = width(); if(n != B.height() or m != B.width()) return false; for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) if((*this)[i][j] != B[i][j]) return false; return true; } Matrix operator+ (const Matrix &B) const{ return (Matrix(*this) += B); } Matrix operator- (const Matrix &B) const{ return (Matrix(*this) -= B); } Matrix operator* (const Matrix &B) const{ return (Matrix(*this) *= B); } Matrix operator^ (const long long &k) const{ return (Matrix(*this) ^= k); } Matrix &operator+= (const T &t){ int n = height(), m = width(); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] += t; return *this; } Matrix &operator-= (const T &t){ int n = height(), m = width(); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] -= t; return *this; } Matrix &operator*= (const T &t){ int n = height(), m = width(); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] *= t; return *this; } Matrix &operator/= (const T &t){ int n = height(), m = width(); for(int i = 0; i < n; i++) for(int j = 0; j < m; j++) (*this)[i][j] /= t; return *this; } Matrix operator+ (const T &t) const{ return (Matrix(*this) += t); } Matrix operator- (const T &t) const{ return (Matrix(*this) -= t); } Matrix operator* (const T &t) const{ return (Matrix(*this) *= t); } Matrix operator/ (const T &t) const{ return (Matrix(*this) /= t); } friend std::ostream &operator<< (std::ostream &os, Matrix &p){ size_t n = p.height(), m = p.width(); for(int i = 0; i < n; i++){ os << '['; for(int j = 0; j < m; j++) os << p[i][j] << (j == m - 1 ? "]\n" : ","); } return (os); } T determinant(){ Matrix B(*this); size_t n = height(), m = width(); assert(n == m); T ret = 1; for(int i = 0; i < n; i++){ int idx = -1; for(int j = i; j < n; j++) if(B[j][i] != 0) idx = j; if(idx == -1) return 0; if(i != idx){ ret *= -1; swap(B[i], B[idx]); } ret *= B[i][i]; T vv = B[i][i]; for(int j = 0; j < n; j++) B[i][j] /= vv; for(int j = i + 1; j < n; j++){ T a = B[j][i]; for(int k = 0; k < n; k++){ B[j][k] -= B[i][k] * a; } } } return ret; } }; //ModInt template struct ModInt { ll x; ModInt() : x(0) {} ModInt(ll x_) { if ((x = x_ % mod + mod) >= mod) x -= mod; } ModInt& operator+=(ModInt rhs) { if ((x += rhs.x) >= mod) x -= mod; return *this; } ModInt& operator-=(ModInt rhs) { if ((x -= rhs.x) < 0) x += mod; return *this; } ModInt& operator*=(ModInt rhs) { x = (unsigned long long)x * rhs.x % mod; return *this; } ModInt& operator/=(ModInt rhs) { x = (unsigned long long)x * rhs.inv().x % mod; return *this; } ModInt operator-() const { return -x < 0 ? mod - x : -x; } ModInt operator+(ModInt rhs) const { return ModInt(*this) += rhs; } ModInt operator-(ModInt rhs) const { return ModInt(*this) -= rhs; } ModInt operator*(ModInt rhs) const { return ModInt(*this) *= rhs; } ModInt operator/(ModInt rhs) const { return ModInt(*this) /= rhs; } ModInt &operator++ () { *this += 1; return *this;} ModInt operator++ (int) { *this += 1; return *this - 1;} ModInt &operator-- () { *this -= 1; return *this;} ModInt operator-- (int) { *this -= 1; return *this + 1;} bool operator==(ModInt rhs) const { return x == rhs.x; } bool operator!=(ModInt rhs) const { return x != rhs.x; } bool operator<=(ModInt rhs) const { return x <= rhs.x; } bool operator>=(ModInt rhs) const { return x >= rhs.x; } bool operator<(ModInt rhs) const { return x < rhs.x; } bool operator>(ModInt rhs) const { return x > rhs.x; } ModInt inv() const { return pow(*this, mod - 2); } friend ostream& operator<<(ostream& s, ModInt a) { s << a.x; return s; } friend istream& operator>>(istream& s, ModInt& a) { s >> a.x; return s; } }; int main(){ INT(n); static int m; cin >> m; using mint = ModInt; Matrix A(2, 2, 1ll), B(2, 1); A[1][1] = 0; B[0][0] = 1; Matrix C = (A^(n - 1)) * B; print(C[1][0]); }