Statement

Giorgio and Alessandro want to play Risiko with an unorthodox ruleset. There are N countries, numbered from 0 to N-1, each with a strength S_i. Before the start of the game, the countries are assigned to K players, indexed from 0 to K-1. Each country is assigned to exactly one player, and two adjacent countries cannot be assigned to the same player. The strength of a player is the sum of the strengths of the countries assigned to them. The development index of a player is the number of countries they have, multiplied by 10^9. The imbalance of the game is the difference between the strength of the strongest player and that of the weakest one, plus the difference between the development index of the most developed player and that of the least developed one. Everybody wants the game to be as balanced as possible, i.e., they want to minimize the imbalance, but they are having a hard time doing so. Can you help them find an assignment of countries which is as balanced as possible?