ZI. Maximum Subarray Sum II
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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

Constraints:

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

Print one integer: the maximum subarray sum.

Example
Input
8 1 2
-1 3 -2 5 3 -5 2 2
Output
8