Stick Difference

You are given n sticks with lengths a_1,a_2,\dots,a_n. You must make exactly k cuts to the sticks, so that the number of sticks becomes n + k. After making the cuts, the difference between the length of the longest and shortest sticks should be as small as possible. Your task is to compute the smallest possible difference for all amounts k=1,2,\dots,m. The cuts must keep the lengths of the stick