K-Way Merge with Heap

$1.$ Initialize a min-heap with the first element from each list (along with list index and position).

$2.$ Extract the minimum. The extracted value is the next element in the merged output.

$3.$ If that list has more elements, insert the next one into the heap.

$4.$ Repeat until heap is empty. The heap always has at most $k$ elements. Each of the $n$ total elements is inserted and extracted once. Total: $O(n \log k)$.