USACO

USACO 2016 January Contest, Silver

Problem 1. Angry Cows

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Bessie the cow has designed what she thinks will be the next big hit video game: "Angry Cows". The premise, which she believes is completely original, is that the player shoots cows with a slingshot into a one-dimensional scene consisting of a set of hay bales located at various points on a number line. Each cow lands with sufficient force to detonate the hay bales in close proximity to her landing site. The goal is to use a set of cows to detonate all the hay bales.

There are $N$ hay bales located at distinct integer positions $x_1, x_2, \ldots, x_N$ on the number line. If a cow is launched with power $R$ landing at position $x$ , this will causes a blast of "radius $R$ ", destroying all hay bales within the range $x-R \ldots x+R$ .

A total of $K$ cows are available to shoot, each with the same power $R$ . Please determine the minimum integer value of $R$ such that it is possible to use the $K$ cows to detonate every single hay bale in the scene.

INPUT FORMAT (file angry.in):

The first line of input contains

$N$ (

$1 \leq N \leq 50,000$ ) and

$K$ (

$1 \leq K \leq 10$ ). The remaining

$N$ lines all contain integers

$x_1 \ldots x_N$ (each in the range

$0 \ldots 1,000,000,000$ ).

OUTPUT FORMAT (file angry.out):

Please output the minimum power

$R$ with which each cow must be launched in order to detonate all the hay bales.

SAMPLE INPUT:

SAMPLE OUTPUT:

Problem credits: Brian Dean

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