Statement

You find an old game of monopoly in your attic and you decide to play it against Carlo. You don't like to lose, so you decide to use your magic dice to cheat. The game is played on a board, made of N cells arranged in a circle. The cells are numbered from 0 to N-1, with cells N-1 and 0 being adjacent. Each cell has a tax value T_i associated with it. Every time a player lands on a cell, he has to pay the tax value of that cell (the tax value can be negative, meaning that the player receives money). Carlo starts on cell 0 and will play K turns of monopoly. Each turn he rolls two 6-sided dice and moves forward by the sum of the two values. He then pays the tax value of the cell he lands on. If the two dice value are equal, after moving and paying, he must continue and roll the dice again. Carlo can move at most 3 times in a single turn, then his turn automatically ends (even if the 2 dice values are equal)...