Maximum Window Sum

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

5 3
1 -2 3 -4 5

4

Explanation

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

Example 2

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

610