#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint1000000007; template struct Mat: std::array, N> { friend Mat operator*(const Mat& A, const Mat& B) { Mat C = {}; for(int i = 0; i < N; i++) { for(int k = 0; k < N; k++) { for(int j = 0; j < N; j++) { C[i][j] += A[i][k] * B[k][j]; } } } return C; } friend std::array operator*(const Mat& A, const std::array& v) { std::array x = {}; for(int i = 0; i < N; i++) for(int j = 0; j < N; j++) x[i] += A[i][j] * v[j]; return x; } friend Mat operator+(const Mat& A, const Mat& B) { Mat C; for(int i = 0; i < N; i++) { for(int j = 0; j < N; j++) { C[i][j] = A[i][j] + B[i][j]; } } return C; } Mat& operator*=(const Mat& A) { return *this = *this * A; } Mat& operator+=(const Mat& A) { for(int i = 0; i < N; i++) { for(int j = 0; j < N; j++) { (*this)[i][j] += A[i][j]; } } } static Mat I() { Mat X = {}; for(int i = 0; i < N; i++) X[i][i] = 1; return X; } Mat pow(long long k) const { assert(k >= 0); auto X = *this; auto Y = I(); while(k) { if (k & 1) Y *= X; k >>= 1; if (k) X *= X; } return Y; } Mat inv() const { auto X = *this; auto Y = I(); for(int p = 0; p < N; p++) { bool ok = false; for(int i = p; i < N; i++) { if (X[i][p] != T()) { ok = true; if (i != p) { // std::swap(X[i], X[p]); for(int j = p; j < N; j++) std::swap(X[i][j], X[p][j]); std::swap(Y[i], Y[p]); } break; } } assert(ok); T c = 1 / X[p][p]; for(int j = p; j < N; j++) X[p][j] *= c; for(int j = 0; j < N; j++) Y[p][j] *= c; for(int i = 0; i < N; i++) if (i != p) { T c = X[i][p]; for(int j = p; j < N; j++) X[i][j] -= c * X[p][j]; for(int j = 0; j < N; j++) Y[i][j] -= c * Y[p][j]; } } return Y; } void elim() { auto& X = *this; int i_next = 0; for(int p = 0; p < N; p++) { bool found = false; for(int i = i_next; i < N; i++) { if (X[i][p] != T()) { found = true; if (i != i_next) swap(X[i], X[i_next]); break; } } if (!found) continue; auto mul = X[i_next][p].inv(); for (int j = p; j < N; j++) X[i_next][j] *= mul; for(int i = i_next + 1; i < N; i++) { T mul = X[i][p]; for (int j = p; j < N; j++) X[i][j] -= X[i_next][j] * mul; } i_next++; } return; } friend std::ostream& operator<<(std::ostream& os, const Mat& A) { for(int i = 0; i < N; i++) for(int j = 0; j < N; j++) os << A[i][j] << " \n"[j + 1 == N]; return os; } }; std::default_random_engine gen(std::chrono::system_clock::now().time_since_epoch().count()); using dist_type = std::uniform_int_distribution<>; using param_type = dist_type::param_type; int RI(int L, int R) { assert(L < R); return dist_type(L, R - 1)(gen); } } int main() { ios::sync_with_stdio(false); cin.tie(0); int a[2][2], b[2][2]; rep(i, 2) rep(j, 2) cin >> a[i][j]; rep(i, 2) rep(j, 2) cin >> b[i][j]; Mat m; m[0] = {a[0][0] - b[0][0], a[1][0], -b[0][1], 0}; m[1] = {a[0][1], a[1][0] - b[0][0], 0, -b[0][1]}; m[2] = {-b[1][0], 0, a[0][0] - b[1][1], a[1][0]}; m[3] = {0, -b[1][0], a[0][1], a[1][1] - b[1][1]}; m.elim(); if (m[3][3] != 0) { cout << "No\n"; return 0; } bool ok = false; rep(_, 10) { int rank = 4; while (rank && m[rank-1] == array{}) rank--; int r = 3; mint v[4]; rrep(i, rank) { int j = 0; while (m[i][j] == 0) j++; while (r > j) v[r--] = RI(0, mint::mod()); for (int jj = j + 1; jj < 4; jj++) v[r] -= m[i][jj] * v[jj]; r--; } while (r >= 0) v[r--] = RI(0, mint::mod()); // rep(i, 4) cout << v[i].val() << " \n"[i + 1 == 4]; if (v[0] * v[3] != v[1] * v[2]) { ok = true; break; } } cout << (ok ? "Yes\n" : "No\n"); }