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Competitions

# Running

The cows are trying to become better athletes, so Bessie is running on a track for exactly n 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 di and her exhaustion factor will increase by 1, but must never be allowed to exceed m. If she chooses to rest, her exhaustion factor will decrease by 1 for each minute she rests. 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.

#### Input

First line contains two integer n (1n104) and m (1m500). Next n lines contains integers d1, d2, ..., dn (1di1000).

#### Output

Print a single integer representing the largest distance Bessie can run while satisfying the conditions.

Time limit 1 second
Memory limit 128 MiB
Input example #1
5 2
5
3
4
2
10

Output example #1
9

Source 2008 USACO January Silver