A10109. More Cowbell

Kevin Sun wants to move his precious collection of $n$ cowbells from Naperthrill to Exeter, where there is actually grass instead of corn. Before moving, he must pack his cowbells into $k$ boxes of a fixed size. In order to keep his collection safe during transportation, he won't place more than two cowbells into a single box. Since Kevin wishes to minimize expenses, he is curious about the smallest size box he can use to pack his entire collection.

Kevin is a meticulous cowbell collector and knows that the size of his $i$ -th ( $1<=i<=n$ ) cowbell is an integer $s_{i}$ . In fact, he keeps his cowbells sorted by size, so $s_{i-1}<=s_{i}$ for any $i>1$ . Also an expert packer, Kevin can fit one or two cowbells into a box of size $s$ if and only if the sum of their sizes does not exceed $s$ . Given this information, help Kevin determine the smallest $s$ for which it is possible to put all of his cowbells into $k$ boxes of size $s$ .

The first line of the input contains two space-separated integers $n$ and $k$ ( $1<=n<=2·k<=100000$ ), denoting the number of cowbells and the number of boxes, respectively.

The next line contains $n$ space-separated integers $s_{1},s_{2},...,s_{n}$ ( $1<=s_{1}<=s_{2}<=...<=s_{n}<=1000000$ ), the sizes of Kevin's cowbells. It is guaranteed that the sizes $s_{i}$ are given in non-decreasing order.

Print a single integer, the smallest $s$ for which it is possible for Kevin to put all of his cowbells into $k$ boxes of size $s$ .

In the first sample, Kevin must pack his two cowbells into the same box.

In the second sample, Kevin can pack together the following sets of cowbells: ${2,3}$ , ${5}$ and ${9}$ .

In the third sample, the optimal solution is ${3,5}$ and ${7}$ .