@Dave,Balaji,Samby.. Without the matrix exponentiation, the time is not possible, and without using the intermediate modulo operater as suggested by Dave, the value cannot be accommodated, as the 300th fibinocci number alone comes to --> 222232244629420445529739893461909967206666939096499764990979600 So, a mix of both are needed.. I'll try to look into this. any alternate solution you can think of?
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