To find out how the computational time differs between the variables K and N, I suggest you analyze your implementation of the algorithm. Different algorithms can have different computational times for variables.
An easy example is by looking at the computational time for the variable n in sorting algorithms, in which n is the size of the list of numbers you wish to sort (in either ascending or descending order). A multitude of algorithms have been developed to sort a list of n random numbers and the computational time depends on the implementation of the algorithm. Using the BubbleSort algorithm gives a computational time of $O(n^2)$, while the HeapSort algorithm has a computational time of $O(n \times log(n))$.
After implementing the secret sharing scheme, you can analyze how the computational load changes by increasing either K or N and figure out the computational time.