Electrostatics: Finding possible value of charge

1. The problem statement, all variables and given/known data
Two small particles have electric charges of equal magnitude and opposite signs. The masses of the particles are m and 2m. Initially, the distance between the particles is d, and the velocities of the particles have equal magnitude v. However, the velocity of particle 2m is directed away from particle m, whereas the velocity of particle m is directed perpendicular to the line connecting the particles. In the subsequent motion of the particles, they are found to be at a distance 3d from each other—twice! Find the possible values of the charge of each particle.

3. The attempt at a solution

I can apply conservation of energy and conservation of angular momentum for this problem. But how do I know what will be the direction of final velocity vectors?

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