Great find indeed. There were plenty of well thought-out challenges and I just wish I had more time to dedicate to them.

One curious question, though… (Google has failed me)
For many of the challenges, there was a note to output the results modulo 1000000007. (to prevent overflow, apparently) What I don’t understand is:
What does that even accomplish? I would reason that is no better an answer than % 1000000007.
What’s significant about the number choice 1000000007?

It is the first 10-digital prime number. In some of such problems to compute the result modular inverses are needed and it helps very much that this number is prime. Also this number should be large enough since otherwise modular inverses technique may fail in some situations.

In fact any prime number less then 2^30 will be fine in order to prevent possible overflows. But this one can be easily written as 10^9+7.

This reasoning almost uniquely determined this number