Maximum Subarray Sum II

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