Asking help for a short but funny problem from 2021 ICPC Shannxi invitational problem E

Revision en2, by fried-chicken, 2021-11-25 10:57:41

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:

  1. N is larger than 1e8;
  2. N is smaller than 1e13;
  3. (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.

Sample input

2

494

997

Sample output

1000001586369

1000001980150

Tags math, constructive, help

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en3 English fried-chicken 2021-11-25 19:03:31 97
en2 English fried-chicken 2021-11-25 10:57:41 6 (published)
en1 English fried-chicken 2021-11-25 10:57:06 779 Initial revision (saved to drafts)