How to solve this Fibonacci Problem — FRSKH?

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SPOJ — FRSKH
The problem requires to efficiently compute

$\text{[math]}$

The constraints are:
$\text{[math]}$
I have solved the easier version with constraint on $\text{[math]}$ and same constrains on $\text{[math]}$
M can be optimized using Pisano Period
N can be optimized using Fast Doubling/Matrix Exponentiation
The issue is constraint on K, which I cant figure a way to optimize. How can we resolve this issue?

-synx-'s blog