#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp" using namespace std; #include #line 1 "/Users/noya2/Desktop/Noya2_library/template/inout.hpp" namespace noya2 { template concept Scanable = requires (ifstream &is, T &a){ is >> a; }; template concept Printable = requires (ofstream &os, T &a){ os << a; }; template istream &operator>>(istream &is, vector &v); template ostream &operator<<(ostream &os, const vector &v); template requires Scanable && Scanable istream &operator>>(istream &is, pair &p){ is >> p.first >> p.second; return is; } template requires Printable && Printable ostream &operator<<(ostream &os, const pair &p){ os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, vector &v){ for (auto &x : v) is >> x; return is; } template ostream &operator<<(ostream &os, const vector &v){ int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } void in() {} template void in(Scanable &t, U &...u){ cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const Printable &t, const U &...u){ cout << t; if (sizeof...(u)) cout << sep; out(u...); } template void out(const vector> &vv){ int s = (int)vv.size(); for (int i = 0; i < s; i++) out(vv[i]); } struct IoSetup { IoSetup(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetup_noya2; } // namespace noya2 #line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp" namespace noya2{ const int iinf = 1'000'000'007; const long long linf = 2'000'000'000'000'000'000LL; const long long mod998 = 998244353; const long long mod107 = 1000000007; const long double pi = 3.14159265358979323; const vector dx = {0,1,0,-1,1,1,-1,-1}; const vector dy = {1,0,-1,0,1,-1,-1,1}; const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const string alp = "abcdefghijklmnopqrstuvwxyz"; const string NUM = "0123456789"; void yes(){ cout << "Yes\n"; } void no(){ cout << "No\n"; } void YES(){ cout << "YES\n"; } void NO(){ cout << "NO\n"; } void yn(bool t){ t ? yes() : no(); } void YN(bool t){ t ? YES() : NO(); } } // namespace noya2 #line 1 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp" namespace noya2{ unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){ if (a == 0 || b == 0) return a + b; int n = __builtin_ctzll(a); a >>= n; int m = __builtin_ctzll(b); b >>= m; while (a != b) { int mm = __builtin_ctzll(a - b); bool f = a > b; unsigned long long c = f ? a : b; b = f ? b : a; a = (c - b) >> mm; } return a << min(n, m); } template T gcd_fast(T a, T b){ return static_cast(inner_binary_gcd(abs(a),abs(b))); } long long sqrt_fast(long long n) { if (n <= 0) return 0; long long x = sqrt(n); while ((x + 1) * (x + 1) <= n) x++; while (x * x > n) x--; return x; } template T floor_div(const T n, const T d) { assert(d != 0); return n / d - static_cast((n ^ d) < 0 && n % d != 0); } template T ceil_div(const T n, const T d) { assert(d != 0); return n / d + static_cast((n ^ d) >= 0 && n % d != 0); } template void uniq(vector &v){ sort(v.begin(),v.end()); v.erase(unique(v.begin(),v.end()),v.end()); } template inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline bool range(T l, T x, T r){ return l <= x && x < r; } } // namespace noya2 #line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp" #define rep(i,n) for (int i = 0; i < (int)(n); i++) #define repp(i,m,n) for (int i = (m); i < (int)(n); i++) #define reb(i,n) for (int i = (int)(n-1); i >= 0; i--) #define all(v) (v).begin(),(v).end() using ll = long long; using ld = long double; using uint = unsigned int; using ull = unsigned long long; using pii = pair; using pll = pair; using pil = pair; using pli = pair; namespace noya2{ /* ~ (. _________ . /) */ } using namespace noya2; #line 2 "c.cpp" #line 2 "/Users/noya2/Desktop/Noya2_library/math/matrix.hpp" #line 4 "/Users/noya2/Desktop/Noya2_library/math/matrix.hpp" namespace noya2{ template struct Matrix{ int rows, cols; vector> m; Matrix (int h = 0, int w = -1, T init = T(0)) : m(h,vector((w == -1 ? h : w),init)){ rows = h, cols = (w == -1 ? h : w); } Matrix (vector> _init) : m(_init), rows(_init.size()), cols(_init.at(0).size()){} vector& operator[](const int i) const {return m[i];} vector& operator[](const int i) {return m[i];} Matrix &operator+= (const Matrix &r){ assert(this->rows == r.rows && this->cols == r.cols); for (int i = 0; i < r.rows; ++i){ for (int j = 0; j < r.cols; ++j){ m[i][j] += r.m[i][j]; } } return *this; } Matrix &operator-= (const Matrix &r){ assert(this->rows == r.rows && this->cols == r.cols); for (int i = 0; i < r.rows; ++i){ for (int j = 0; j < r.cols; ++j){ m[i][j] -= r.m[i][j]; } } return *this; } Matrix &operator*= (const Matrix &r){ assert(this->cols == r.rows); Matrix res(rows, r.cols); for (int i = 0; i < rows; ++i){ for (int j = 0; j < r.cols; ++j){ for (int k = 0; k < r.rows; ++k){ res[i][j] += m[i][k] * r.m[k][j]; } } } return *this = res; } Matrix operator+ (const Matrix &r) const {return Matrix(*this) += r;} Matrix operator- (const Matrix &r) const {return Matrix(*this) -= r;} Matrix operator* (const Matrix &r) const {return Matrix(*this) *= r;} bool operator== (const Matrix &r){ if (rows != r.rows || cols != r.cols) return false; for (int i = 0; i < r.rows; ++i){ for (int j = 0; j < r.cols; ++j){ if (m[i][j] != r.m[i][j]) return false; } } return true; } Matrix& operator+=(const T &r){ for (int i = 0; i < rows; ++i){ for (int j = 0; j < cols; ++j){ m[i][j] += r; } } return *this; } Matrix& operator-=(const T &r){ for (int i = 0; i < rows; ++i){ for (int j = 0; j < cols; ++j){ m[i][j] -= r; } } return *this; } Matrix& operator*=(const T &r){ for (int i = 0; i < rows; ++i){ for (int j = 0; j < cols; ++j){ m[i][j] *= r; } } return *this; } Matrix& operator/=(const T &r){ for (int i = 0; i < rows; ++i){ for (int j = 0; j < cols; ++j){ m[i][j] /= r; } } return *this; } Matrix operator+ (const T &r) const {return Matrix(*this) += r;} Matrix operator- (const T &r) const {return Matrix(*this) -= r;} Matrix operator* (const T &r) const {return Matrix(*this) *= r;} Matrix operator/ (const T &r) const {return Matrix(*this) /= r;} Matrix e(){ assert(this->rows == this->cols); Matrix res(this->rows, this->rows); for (int i = 0; i < rows; ++i) res[i][i] = 1; return res; } Matrix pow(long long n){ assert(this->rows == this->cols); if (n == 0) return e(); Matrix f = pow(n / 2); Matrix ans = f * f; if (n % 2 == 1) ans *= *this; return ans; } // for T = int, long long, double, long double void show(){ for (int i = 0; i < rows; ++i){ for (int j = 0; j < cols; ++j){ cout << m[i][j] << (j+1 == this->cols ? "\n" : " "); } } } T determinant() const { Matrix B(*this); assert(rows == cols); T ret = 1; for (int i = 0; i < rows; i++) { int idx = -1; for (int j = i; j < cols; j++) { if (B[j][i] != 0) { idx = j; break; } } if (idx == -1) return 0; if (i != idx) { ret *= T(-1); swap(B[i], B[idx]); } ret *= B[i][i]; T inv = T(1) / B[i][i]; for (int j = 0; j < cols; j++) { B[i][j] *= inv; } for (int j = i + 1; j < rows; j++) { T a = B[j][i]; if (a == 0) continue; for (int k = i; k < cols; k++) { B[j][k] -= B[i][k] * a; } } } return ret; } }; } // namespace noya2 #line 4 "c.cpp" void solve(){ vector a(2,vector(2)); in(a); Matrix b(2); rep(i,2) rep(j,2) b[i][j] = a[i][j]; b.pow(3).show(); } int main(){ int t = 1; //in(t); while (t--) { solve(); } }