Since we only care about the execution time of COMPARE(), the solution is to call COMPARE() as less as possible, yet achieving our goal, which is targeting and sorting the first k largest numbers in a given set of n numbers

1. Iterate through n numbers: i_1, i_2,...,i_n
2. Compare them with the smallest number k_smallest in first k numbers
3. If i is larger than k_smallest, use binary search to find the best position in k for i, then push all numbers in k that are smaller than i one position forward, so that there will be a empty space for i to insert into.
4. Else if i is smaller k_smallest, skip it
5. Repeat steps above until all n numbers are examined.

From the steps we see above, only step 2 and 3 are required to use COMPARE(), therefore, we manage to dramatically reduce our calling times for COMPARE() and successfully complete our comparing tasks.