I-Will-Windra has entered a racing contest! The racetrack can be represented as two arrays of integers ~a~ and ~b~, both of length ~n~. When I-Will-Windra is at position ~i~, they can jump either ~a[i]~ positions to the left or right, assuming it is within the bounds of the array. Furthermore, this move costs them ~b[i]~.

As I-Will-Windra's FIT2004 tutor, you want to help them. Given starting positions ~x~ and ~y~, what is the minimum cost by which I-Will-Windra can get from ~x~ to ~y~. If this is not possible, output -1 instead.

Note that starting positions are 0 indexed.

Input Format

The first line of input will consist of three integers, ~n~, ~x~ and ~y~. The next two lines will each consist of ~n~ integers, representing ~a~ and ~b~ respectively.

Output Format

The output should consist of a single integer, the minimum cost or -1 if it is impossible.

Example Input

5 4 2
3 3 1 3 2
533 776 812 489 523

Example Output

523

Example Explanation

This can be completed in one jump, from index 4 to index 2 (of cost 523).

Constraints

~2 \le n \le 1e5~

~0 \le x,y \le n-1~

~1 \le a[i] \le n~

~1 \le b[i] \le 30~