Problem Statement

An integer sequence where no two adjacent elements are the same is called a good sequence.

You are given two good sequences of length $N$: $A=(A_1,A_2,\dots,A_N)$ and $B=(B_1,B_2,\dots,B_N)$. Each element of $A$ and $B$ is between $0$ and $M-1$, inclusive.

You can perform the following operations on $A$ any number of times, possibly zero:

• Choose an integer $i$ between $1$ and $N$, inclusive, and perform one of the following:
• Set $A_i \leftarrow (A_i + 1) \bmod M$.
  • Set $A_i \leftarrow (A_i - 1) \bmod M$. Here, $(-1) \bmod M = M - 1$.

However, you cannot perform an operation that makes $A$ no longer a good sequence.

Determine if it is possible to make $A$ equal to $B$, and if it is possible, find the minimum number of operations required to do so.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $2 \leq M \leq 10^6$
• $0\leq A_i,B_i< M(1\leq i\leq N)$
• $A_i\ne A_{i+1}(1\leq i\leq N-1)$
• $B_i\ne B_{i+1}(1\leq i\leq N-1)$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N M
A_1 A_2 \dots A_N
B_1 B_2 \dots B_N

Output

If the goal is unachievable, print -1.

Otherwise, print the minimum number of operations required as an integer.