Initially, the problem 1255B - Fridge Lockers was with no constraint $$$m \le n$$$ (just $$$m \le 2000$$$). Almost all participants (and me) invented wrong solution like: "make a cycle plus take the cheapest edge $$$m-n$$$ times". The counter-example is $$$n=5$$$, $$$m=6$$$ and prices are $$$3, 4, 1, 4, 5$$$. Look into the picture:
It was really unexpected for my intuition (and, of course, failed a proof).
Do you know the solution for this case?