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