Maximum Subarray Sum II

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

Input

The first input line has three integers $nn$, $aa$ and $bb$: the size of the array and the minimum and maximum subarray length.

The second line has $nn$ integers $x_1,x_2,\dots ,x_{n}x\_1,x\_2,\backslash dots,x\_n$: the array values.

Output

Print one integer: the maximum subarray sum.