Placeholder

#3956

Angry Cows 2초 512MB

문제

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.

Problem credits: Brian Dean


입력

The first line of input contains NN (1≤N≤50,0001 \leq N \leq 50,000) and KK (1≤K≤101 \leq K \leq 10). The remaining NN lines all contain integers x1…xNx_1 \ldots x_N (each in the range 0…1,000,000,0000 \ldots 1,000,000,000).



출력

Please output the minimum power RR with which each cow must be launched in order to detonate all the hay bales.


예제1

입력
7 2
20
25
18
8
10
3
1
출력
5

출처

USACO 2016 January Silver


역링크 공식 문제집만

로그인해야 코드를 작성할 수 있어요.