A828. I Would Walk 500 Miles--Gold

Farmer John wants to divide his $N$ cows $(N \leq 7500)$, conveniently
numbered $1 \ldots N$, into $K$ non-empty groups ($2 \leq K \leq N$) such that
no two cows from two different groups can interact with each other without
walking some number of miles. Cow $x$ and Cow $y$ (where $1 \leq x < y \leq
N$) are willing to walk $(2019201913x + 2019201949y)\text{ mod } 2019201997$
miles to see each other.
Given a division of the $N$ cows into $K$ non-empty groups, let $M$ be the
minimum of the number of miles any two cows in two different groups are
willing to walk to see each other. To test the cows' devotion to each other,
Farmer John wants to optimally divide the $N$ cows into $K$ groups such that
$M$ is as large as possible. The memory limit for this problem is set to
512MB, above the usual 256MB limit.

The input is just one line, containing $N$ and $K$, separated by a space.

Print out $M$ in an optimal solution.

In this example, Cow 1 and Cow 2 are willing to walk 2019201817 miles to see
each other. Cow 2 and Cow 3 are willing to walk 2019201685 miles. And Cow 1
and Cow 3 are willing to walk 2019201769 miles. Thus, by grouping the cows
such that 1 is by herself and 2 and 3 are grouped together, $M =
\min(2019201817,2019201769) = 2019201769$ (which is the best we can do here).