For each ordered pair of real numbers (x, y) satisfying

\log _{2}(2 x+y)=\log _{4}\left(x^{2}+x y+7 y^{2}\right),

there is a real number K such that

\log _{3}(3 x+y)=\log _{9}\left(3 x^{2}+4 x y+K y^{2}\right) .

Find the product of all possible values of K.