#include #include using namespace std; using namespace atcoder; #define overload4(_1, _2, _3, _4, name, ...) name #define rep1(n) for(int i = 0; i < (int)(n); ++i) #define rep2(i, n) for(int i = 0; i < (int)(n); ++i) #define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i) #define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i) #define ALL(a) (a).begin(), (a).end() #define Sort(a) (sort((a).begin(), (a).end())) #define RSort(a) (sort((a).rbegin(), (a).rend())) #define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end())) typedef long long int ll; typedef unsigned long long ul; typedef long double ld; typedef vector vi; typedef vector vll; typedef vector vc; typedef vector vst; typedef vector vd; typedef vector vld; typedef pair P; template long long sum(const T& a){ return accumulate(a.begin(), a.end(), 0LL); } template auto min(const T& a){ return *min_element(a.begin(), a.end()); } template auto max(const T& a){ return *max_element(a.begin(), a.end()); } const long long MINF = 0x7fffffffffff; const long long INF = 0x1fffffffffffffff; const long long MOD = 998244353; const long double EPS = 1e-9; const long double PI = acos(-1); template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } 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 istream &operator>>(istream &is, vector &v){ for(T &in : v) is >> in; return is; } template ostream &operator<<(ostream &os, const vector &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; } template ostream &operator<<(ostream &os, const map &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; } template ostream &operator<<(ostream &os, const set &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, const multiset &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, queue q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; } template ostream &operator<<(ostream &os, deque q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; } template ostream &operator<<(ostream &os, stack st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; } template ostream &operator<<(ostream &os, priority_queue pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; } template inline T vin(T& vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; } template inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; } template void in(T&... a){ (cin >> ... >> a); } void out(){ cout << '\n'; } template void out(const T& a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } template void inGraph(vector>& G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } } template struct Matrix{ int n, m; vector val; Matrix(int _n, int _m): n(_n), m(_m), val(_n * _m){} Matrix(const vector>& mat){ n = mat.size(); m = mat[0].size(); val.resize(n * m); for(int i = 0; i < n; ++i){ for(int j = 0; j < m; ++j){ val[i * m + j] = mat[i][j]; } } } static Matrix e(int _n){ Matrix res(_n, _n); for(int i = 0; i < _n; ++i){ res[i][i] = T{1}; } return res; } auto operator[](int i){ return val.begin() + i * m; } auto operator[](int i) const { return val.begin() + i * m; } inline Matrix& operator+=(const Matrix &rhs){ for(int i = 0; i < n * m; ++i){ val[i] += rhs[i]; } return *this; } inline Matrix& operator-=(const Matrix &rhs){ for(int i = 0; i < n * m; ++i){ val[i] -= rhs[i]; } return *this; } inline Matrix operator*(const Matrix &rhs){ assert(m == rhs.n); const int l = rhs.m; Matrix res(n, l); for(int i = 0; i < n; ++i){ for(int j = 0; j < m; ++j){ for(int k = 0; k < l; ++k){ res[i][k] += val[i * m + j] * rhs[j][k]; } } } return res; } inline Matrix& operator*=(const Matrix &rhs){ return *this = *this * rhs; } friend inline Matrix operator+(const Matrix& lhs, const Matrix& rhs) noexcept { return Matrix(lhs) += rhs; } friend inline Matrix operator-(const Matrix& lhs, const Matrix& rhs) noexcept { return Matrix(lhs) -= rhs; } friend inline bool operator==(const Matrix& lhs, const Matrix& rhs) noexcept { return lhs.val == rhs.val; } friend inline bool operator!=(const Matrix& lhs, const Matrix& rhs) noexcept { return lhs.val != rhs.val; } friend inline ostream& operator<<(ostream& os, const Matrix& mat) noexcept { const int _n = mat.n; const int _m = mat.m; for(int i = 0; i < _n; ++i){ for(int j = 0; j < _m; ++j){ os << mat[i][j] << " \n"[j == _m - 1]; } } return os; } Matrix inv() const { Matrix a = *this, b = e(n); for(int i = 0; i < n; ++i){ if(a[i][i] == 0){ for(int j = i + 1; j < n; ++j){ if(a[j][i] != 0){ for(int k = i; k < n; ++k) swap(a[i][k], a[j][k]); for(int k = 0; k < n; ++k) swap(b[i][k], b[j][k]); break; } } } if(a[i][i] == 0) throw "Inverse does not exist."; const T x = T{1} / a[i][i]; for(int k = i; k < n; ++k) a[i][k] *= x; for(int k = 0; k < n; ++k) b[i][k] *= x; for(int j = 0; j < n; ++j){ if(i != j){ const T x = a[j][i]; for(int k = i; k < n; ++k) a[j][k] -= a[i][k] * x; for(int k = 0; k < n; ++k) b[j][k] -= b[i][k] * x; } } } return b; } Matrix pow(long long r) const { if(r == 0) return e(n); if(r < 0) return inv().pow(-r); Matrix res = e(n), a = *this; while(r > 0){ if(r & 1) res *= a; a *= a; r >>= 1; } return res; } Matrix pow2(string &r) const { if(r == "0") return e(n); Matrix res = e(n), a = *this; int siz = r.size(); for(int i = siz - 1; i >= 0; i--){ if(r[i] == '1') res *= a; a *= a; } return res; } T det() const { Matrix a = *this; T res = 1; for(int i = 0; i < n; ++i){ if(a[i][i] == 0){ for(int j = i + 1; j < n; ++j){ if(a[j][i] != 0){ for(int k = i; k < n; ++k){ swap(a[i][k], a[j][k]); } res = -res; break; } } } if(a[i][i] == 0) return 0; res *= a[i][i]; const T x = T{1} / a[i][i]; for(int k = i; k < n; ++k){ a[i][k] *= x; } for(int j = i + 1; j < n; ++j){ const T x = a[j][i]; for(int k = i; k < n; ++k){ a[j][k] -= a[i][k] * x; } } } return res; } // Rotate 90 degrees clockwise Matrix rotate() const { Matrix res(m, n), a = *this; for(int i = 0; i < m; ++i){ for(int j = 0; j < n; ++j){ res[i][j] = a[n - j - 1][i]; } } return res; } }; void input(){ } void solve(){ Matrix mat(2, 2); rep(i, 2) rep(j, 2){ in(mat[i][j]); } out(mat.pow(3)); } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(20); input(); solve(); }