Angry Cows (Silver)

Bessie built a video game called "Angry Cows". The player fires cows from a slingshot into a one dimensional scene that holds hay bales at various points of a number line. A cow lands hard enough to detonate the hay bales near its landing site, and the goal is to detonate every bale.

There are $N$ hay bales at distinct integer positions $x_1, x_2, \ldots, x_N$ on the number line. A cow launched with power $R$ that lands at position $x$ creates a blast of radius $R$ and destroys every hay bale in the range $x-R$ to $x+R$. A cow may land at any point of the number line, and the landing point does not have to be an integer.

You have $K$ cows, each with the same power $R$, and $R$ is an integer. Find the smallest $R$ for which the $K$ cows can detonate every hay bale.

The first line holds $N$ ($1 \le N \le 50{,}000$) and $K$ ($1 \le K \le 10$). Each of the next $N$ lines holds one coordinate $x_i$. Every coordinate is an integer between $0$ and $1{,}000{,}000{,}000$ inclusive, and the coordinates are distinct.

Print the smallest power $R$ that lets the cows detonate every hay bale.