Racing

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 $a[i]$ 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.

Input

The first line of input will consist of three integers, $x$ $y$ and $z$.

The next two lines will each consist of $n$ integers, representing $a$ and $b$ respectively.

Output

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

Constraints

• $2 \le n \le 10^5$
• $0 \le x,y \le n-1$
• $1 \le a[i] \le n$
• $1 \le b[i] \le 30$

Example 1

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

523

Explanation

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