I am practicing previous year question.
I was having problem in understanding the contest analysis of ROUND 1A( C ) 
quesn. 2008

There are different solutions available . I was working on 'solution A' of this 
ques.

It is written Xn=(2*A_n)%1000 , but why did final result is Xn=( 2*A_n +999 
)%1000
why 999 is added again?

and second there is some typing mistake in the python code provided in solutionA
It is written :: return (2 * M_n[0][0] + 999) % 1000
It should be :: return (2 * A_n[0][0] + 999) % 1000

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