Problem Statement

There are $L$ squares lining up horizontally in a row, numbered $1, 2, \ldots, L$ from left to right.

On those squares are $N$ penguins, numbered $1, 2, \ldots, N$ from left to right. Initially, Penguin $i$ is on Square $A_i$. Here, $1 \leq A_1 < A_2 < \ldots < A_N \leq L$ holds.

You can do the following operations any number of times:

• Choose one penguin and slide it to the left or the right. The penguin will keep sliding as long as there is an empty square ahead. It will stop when it reaches a square just before a square occupied by another penguin, or there is no square ahead.

For example, assume that $N=3$, $L=10$, and the penguins are on the squares $(2,3,7)$. Here, if we slide Penguin $2$ to the right, it will move to Square $6$; if we slide Penguin $3$ to the right, it will move to Square $10$.

Your objective is to put Penguin $i$ on Square $B_i$ for every $i$. Here, $1 \leq B_1 < B_2 < \ldots < B_N \leq L$ holds. Determine whether the objective is achievable. If it is achievable, find the minimum number of operations needed.

Constraints

• $1 \leq N \leq 10^5$
• $N \leq L \leq 10^9$
• $1 \leq A_1 < A_2 < \ldots < A_N \leq L$
• $1 \leq B_1 < B_2 < \ldots < B_N \leq L$
• All numbers in input are integers.

Input

Input is given from Standard Input in the following format:

N L
A_1 A_2 \cdots A_N
B_1 B_2 \cdots B_N

Output

If the objective is unachievable, print $-1$; if it is achievable, print the minimum number of operations needed.