Given an array of $n$ integers, your task is to find the maximum sum of values in a contiguous subarray with length between $a$ and $b$.

Input

The first input line has three integers $n$, $a$ and $b$: the size of the array and the minimum and maximum subarray length.

The second line has $n$ integers $x_1,x_2,\dots,x_n$: the array values.

Output

Print one integer: the maximum subarray sum.

Constraints

• $1 \le n \le 2 \cdot 10^5$
• $1 \le a \le b \le n$
• $-10^9 \le x_i \le 10^9$

Example

Input:

8 1 2
-1 3 -2 5 3 -5 2 2

Output:

8