Maximum Flower Sum

You are given several test cases. In each test case, you are provided with n flowers arranged in a row, each having a magical value, and an integer k representing the size of a contiguous segment.

Your task is to compute the maximum possible sum of the magical values for any contiguous segment of exactly k flowers. The test cases are given one after another and the input terminates with a line containing 0 0, which should not be processed.

Note: The solution is expected to use an efficient algorithm (e.g., sliding window) in order to handle larger inputs.

The formula for the sum of a segment starting at index i is given by:

[ S = \sum_{j=i}^{i+k-1}{a_j} ]

where \(a_j\) is the magical value of the j-th flower.

inputFormat

The input consists of multiple test cases. Each test case includes:

• A line with two integers n and k, where n is the number of flowers and k is the segment size.
• A line with n space-separated integers representing the magical values of the flowers.

The input terminates with a test case where n = 0 and k = 0 (this test case should not be processed).

The input is read from standard input (stdin).

outputFormat

For each test case, output a single line containing the maximum sum of any contiguous segment of exactly k flowers. The output for each test case should be printed to standard output (stdout).

## sample

5 3
1 -2 3 4 -1
6 2
-1 2 3 -2 5 1
0 0

6
6

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