Given an array ~a~ of length ~n~ and an integer ~k~, find the maximum possible sum of a contiguous subarray of length exactly ~k~.

Remember that a subarray is a contiguous section of the array.

Input

The first line contains two integers ~n~ and ~k~.

The second line contains ~n~ integers ~a_1, a_2, \dots, a_n~.

Output

Print a single integer: the maximum sum of any contiguous subarray of length exactly ~k~.

Constraints

• ~1 \le k \le n \le 10^5~
• ~-10^3 \le a_i \le 10^3~

Example 1

Input

5 3
1 -2 3 -4 5

Output

4

Explanation

The length-~3~ subarrays have sums ~2~, ~-3~, and ~4~, so the answer is ~4~.

Example 2

Input

8 3
-512 750 27 -532 -940 781 -449 278

Output

610