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B. More Cowbell

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputKevin 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*.

Input

The first line of the input contains two space-separated integers *n* and *k* (1 ≤ *n* ≤ 2·*k* ≤ 100 000), 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} ≤ 1 000 000), the sizes of Kevin's cowbells. It is guaranteed that the sizes *s* _{ i} are given in non-decreasing order.

Output

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*.

Examples

Input

2 1

2 5

Output

7

Input

4 3

2 3 5 9

Output

9

Input

3 2

3 5 7

Output

8

Note

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}.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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