First method:
Use multiple baskets, each basket is a list (in my case, i use vector<int>). Put the date d into the basket numbered d % number_of_baskets. To check the student answer, just pick the basket out and perform binary search. I chose 100 000 as the number of baskets, tried 1 000 000 baskets but it works much worse.

Second method:
Use vector<bool> (not bool array, the later cost 8 times more) to mark numbers under 300 000 000 (actually the vector size can go up to 500 000 000, but for some unknown reason, this smaller size run faster). Create another vector<int> to store the numbers that can't be marked using the bool vector above. Use binary_search to check for existence.

It seem like the IO is bottleneck, I used ios::sync_with_stdio(false) and my program run from ~1.5s to ~0.2s

Edited by author 01.10.2018 12:46