For this problem, you are given an array of positive integers, ~w_1,w_2,\dots,w_n~, and a positive integer ~L~. You can change the position of at most one element in the array to maximize the ~M~ such that ~w_1+w_2+\dots+w_M\leq L~.

Let ~M~ be the initial maximum (i.e. without changing the position of any element, either (~w_1+w_2+\dots+w_M\leq L~ and ~w_1+w_2+\dots+w_M+w_{M+1}> L~) or ~M=n~), and let ~i~ be the index of the element you wish to change position, ~j~ be the index of this element after changing its position, ~w_1',w_2',\dots,w_n'~ be the new array. Consider the following four situations:

Case 1: if ~1\leq i\leq M~, and ~1\leq j\leq M~, then ~w_1'+w_2'+\dots+w_M'=w_1+w_2+\dots+w_M\leq L~ as we just reordered the first ~M~ elements, therefore this doesn't improve our answer.

Case 2: if ~1\leq i\leq M~, and ~M<j\leq n~, then it is optimal to pick the ~i~ with maximum ~w_i~ and move it to the back of the array.

Case 3: if ~M<i\leq n~, and ~1\leq j\leq M~, then it is optimal to pick the ~i~ with minimum ~w_i~ and move it to the front of the array.

Case 4: if ~M<i\leq n~, and ~M<j\leq n~, then moving any ~i~ with ~i>M+1~ to positions ~>M+1~ would have no effect on the answer, moving it to positions ~\leq M+1~ would reduce the problem to case 3. Now consider moving ~i=M+1~, as it potentially might be large and block the entrance to the elevator, so we move it to the back of the array.