Birthday Gift

Time Limit: 1000 ms

Memory Limit: 65535 ms

Description

At zlly's 20-th birthday party, WAVwind shows him a fancy sequence A1, A2, ..., AN. zlly is allowed to select NO MORE than M successive parts as his birthday gift.

It is natural that he wants to know the greatest sum of the selected elements. CAN YOU HELP HIM?

Input

Line 1: two integers N (1 ≤ N ≤ 105) and M (0 ≤ M ≤ 105), the length of sequence and the number of parts can be selected. Line 2: N integers A1, A2, ..., AN (0 ≤ |Ai| ≤ 104), the sequence.

Output

An integer, the greatest sum.

Sample Input

5 2 
2 -3 2 -1 2

Sample Output

5

Hint

Source

NJUSTACMCONTEST--WAVwind

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