We can observe that in order to obtain an average of at least ~K~, your test scores need to add up to a value of at least ~N \times K~. Thus, in the solution, we can keep adding on to this total score until ~N \times K~ is reached.

For the first subtask, we add 1 to the total score each time. We can decide the test score we should add to by iterating through all of the test scores that are below ~M~ and finding the test with the lowest ~y_i~ value. We can then add 1 to that test score.

For the second subtask, we also add 1 to the total score each time. Instead of looping through all the tests this time, we can use a data structure such as a priority queue to help us find the lowest ~y_i~ value faster.

For the third subtask, we can store two values for each test in an array: ~M - x_i~, and ~y_i~. The first value represents the number of points we can increase this test by until it reaches ~M~. The second represents the number of hours you need to study to increase the score by 1 point. Then, we can sort the array to form an array with non-decreasing ~y_i~ values. Then, we traverse the array and keep increasing the total score by ~M - x_i~ until it exceeds ~N \times K~. Finally, we subtract the extra hours that we studied to lower the total score to ~N \times K~.