So,  I just wrote solution with C long double and got WA #5 (Laplacian).
Then I just rewrote it in Python with decimal.py and got WA...#3! Then I started to add more precision to decimal and got TLE #3.
Yeah, I use some epsilon constant and add it to determinant  before convert determinant to integer and get its modulo  10**9.

Lol
FINALLY  understand
I should just made M[row] [col] =LCM

WA#6 now!

http://ideone.com/bHtkjS

Yeah!
I tried this:
3 3
***
*.*
***

And got zero,  not one!
Should correct...

Corrected that input for 3 3.
But WA#6 still!!!
http://ideone.com/KGeDMM

Edited by author 08.05.2017 17:42

WA #8.
I am really frustrated.
http://ideone.com/7nPKN0

That time without fractions.  Used decimal with 1450 digits after point.

Edited by author 08.05.2017 18:47

I realized I need not determinant of a whole matrix but just a minor.
 http://ideone.com/5H6ARH
Submitted corrected solution with Fractions.
Buuut!!  WA #8 still...

ULTIMATELY got it.
It was really fun...
http://ideone.com/CIEdmo