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.

INPUT FORMAT (file angry.in):

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 range0…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:

7 2
20
25
18
8
10
3
1

SAMPLE OUTPUT:

5