This is a problem from 2021 ICPC Shannxi invitational and confuse me a lot. Since this contest have neither place to up-solving nor tutorial, I'm here to ask for idea and help.
The problem is like:
Given a number X, we call another number N is a lucky number to X if:
- N is larger than 1e8;
- N is smaller than 1e13;
- (N!) begins with X.
For example, if we ignore the first constraint, N=10 is a lucky number to X=3628 since (10!)=3628800.
Now, given T testcases, each testcases gives you a X, output any N where N is a lucky number to X.
T is smaller than 200 and X is smaller than 1e5.
UPD: Thanks everybody for helping, I think using stirling's and brute force is the right one.