7881: USACO 2016 January Contest, Silver —— Problem 1. Angry Cows
[Creator : ]
Description
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 $x_1,x_2,…,x_N$ 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 $x−R…x+R$.
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.
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
The first line of input contains N (1≤N≤50,000) and K (1≤K≤10).
The remaining N lines all contain integers $x_1…x_N$ (each in the range 0…1,000,000,000).
The remaining N lines all contain integers $x_1…x_N$ (each in the range 0…1,000,000,000).
Output
Please output the minimum power R with which each cow must be launched in order to detonate all the hay bales.
Sample 1 Input
7 2
20
25
18
8
10
3
1
Sample 1 Output
5