Does Gods mercy contradict justice?

If you define justice as giving everyone what they deserve, then mercy is the opposite of that, either Forgiving them when they could be punished, or "multiplying" their reward. Now if you say someone deserved "mercy", that's justice and not mercy at all because they deserved it. It also can't be that God can be just at sometime and merciful at another, since that would mean he's sometimes unjust. Ditto for some kind of grander scheme of justice involving mercy. Let's not even get into fairness. If god gives mercy whenever he wants and doesn't(which he necessarily can't do for a reason, since if it were reasonable it would be called justice) then that means different people are punished differently for the same crime !