163. Wise King

time limit per test: 0.25 sec.
memory limit per test: 65536 KB
input: standard input
output: standard output

Once upon a time in a country far away lived a king and he had a big kingdom. He was a very wise king but he had one weakness - he could count only up to three.
Nevertheless, he did not consider this to be a really great drawback, since he had a lot of wizards who could count up to one hundred (and some of them, people said, even up to one thousand). But one day the grief came to the kingdom as the outnumbering barbarians started to approach from all sides. And the king then had to make the most important decision in his life. He had to choose which of his sons to make generals that he would send to the borders of the country to lead the army.
However, the king knew that though some of his sons were smart, just like he was, some of them were quite stupid and could only lower army spirits with their wrong decisions. More precisely, he knew about each of his sons his mental potential - an integer number ranging from minus three to three (remember, that the king could count only up to three). He also knew that the chance of his army defeating barbarians was proportional to the sum of some powers of mental potentials of those of his sons that he would make generals (the power exponent was a positive integer number, the same for all his sons and not exceeding three either). Thus he had to choose such a combination of his sons to lead the army, that this sum would be maximal possible.
However, the king himself could not make all appropriate calculations since, for example, the second power (the square) of a number not exceeding three could be greater than three, and therefore he asked you, his most intelligent wizard, to solve this problem.

The first line of the input file contains the number of the sons of the king (integer number less than or equal to one hundred). The second line contains the positive integer number not exceeding three, the exponent in the formula used to calculate the chance of defeating barbarians. The third line contains the list of mental potentials of king's sons - all integer numbers, not greater than three by their absolute value.

Output the only number - the maximal possible chance of defeating barbarians calculated as the sum described.

Sample test(s)

In the first example below the king should choose his first and third sons to be the generals. In this case the chance to defeat barbarians, which is the sum of cubes of mental potentials of these sons, is eight plus one, that is nine.
In the second example sending his son to lead the army causes the sum to be negative, thus he should not do it and the sum would be zero.

Sample input #1
2 -1 1

Sample input #2

Sample output #1

Sample output #2


You can download pdf version of this task here

Author:Andrew Stankevich, Andrew Lopatin, Nikolay Durov, Georgy Korneev
Resource:ACM ICPC 2002-2003 NEERC, Northern Subregion
Date:November, 2002

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