I have tried to solve The Table Tennis Question but I got the following mistake.

When k = 666666, a= 6666666, b= 666665

The answer is -1. But, I don't understand why the answer isn't 10. The given configuration is reachable if one player wins ten sets and scores 6666660 and then 6 more points while his opponent scores that many points. Why is the answer -1 in this case ?

Thanks.