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 si. In fact, he keeps his cowbells sorted by size, so si-1≤si 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 s1,s2,...,sn (1≤s1≤s2≤...≤sn≤1000000), the sizes of Kevin's cowbells. It is guaranteed that the sizes si 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.
2 1
2 5
7
4 3
2 3 5 9
9
3 2
3 5 7
8
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}.