Two blocks slide toward each other on a frictionless surface. Block $1$ moves to the right with a velocity of $4a,$ and block $2$ moves to the left with a velocity of $a,$ where $a$ is a parameter. After the blocks collide, if block $1$ travels to the right with a velocity of $a,$ and block $2$ travels to the right with a velocity of $5a,$ what is the ratio of the mass of block $1$ to the mass of block $2(($:$\frac{m_1}{m_2}\}$