[INOI1301] Calvins Game (INOI 2013: India)

Problem in short: You are given an array a of length N. You start at position k. In the forward phase, you make jumps of size 1 or 2 towards the right. Then in the backward phase, you make jumps of size 1 of 2 towards the left till you reach position 1. Your score is the sum of the values in the array where you landed after each jump. What is the maximum score you can make?

Indian National Olympiad in Informatics (INOI) is round 2 out of 3 (i.e. intermediate) for selection into Indian IOI team.