Running and Resting           runrest.X

The cows are trying to become better athletes, so Bessie is running on a
track for exactly N (1 <= N <= 10,000) minutes. During each minute, she can
choose to either run or rest for the whole minute.

The ultimate distance Bessie runs, though, depends on her 'exhaustion
factor', which starts at 0. When she chooses to run in minute i, she will
run exactly a distance of D_i (1 <= D_i <= 1,000) and her exhaustion factor
will increase by 1 -- but must never be allowed to exceed M (1 <= M <=
500).  If she chooses to rest, her exhaustion factor will decrease by 1 for
each minute she rests, but can never go below 0. She cannot commence
running again until her exhaustion factor reaches 0. At that point, she
can choose to run or rest.

At the end of the N minute workout, Bessie's exhaustion factor must be
exactly 0, or she will not have enough energy left for the rest of the day.

Find the maximal distance Bessie can run.

PROBLEM NAME: runrest

INPUT FORMAT:

* Line 1: Two space-separated integers: N and M

* Lines 2..N+1: Line i+1 contains the single integer: D_i

SAMPLE INPUT:

5 2
5
3
4
2
10

OUTPUT FORMAT:

* Line 1: A single integer representing the largest distance Bessie
        can run while satisfying the conditions.

SAMPLE OUTPUT:

9

OUTPUT DETAILS:

Bessie runs during the first minute (distance=5), rests during the second
minute, runs for the third (distance=4), and rests for the fourth and
fifth. Note that Bessie cannot run on the fifth minute because she would
not end with an exhaustion factor of 0.