Numerical Methods: Euler to Runge–Kutta · Challenge problem

A two-stage explicit Runge–Kutta method has the form $k_1 = f(t_n, y_n)$, $k_2 = f(t_n + c h,\ y_n + c h k_1)$, $y_{n+1} = y_n + h(a k_1 + b k_2)$. Take $c = \dfrac{1}{3}$. For which value of $a$ (with the matching $b$) is the method second-order accurate, that is, does one step agree with the Taylor expansion of the exact solution through the $h^2$ term for every smooth $f$? Express your answer as a common fraction.