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

Example Output

8