Read problem statements in [Vietnamese],
[Bengali], [Mandarin Chinese], and [Russian] as well.

There are $N$ cities in Chefland numbered from $1$ to $N$ and every city has a railway station. Some cities have a train and each city has at most one train originating from it. The trains are represented by an array $A$, where $A_{i} = 0$ means the $i$-th city doesn't have any train originating from it, $A_{i} = 1$ means the train originating from the $i$-th city is moving right (to a higher numbered city), and $A_{i} = 2$ means the train originating from the $i$-th city is moving left (to a lower numbered city).

Each train keeps on going forever in its direction and takes $1$ minute to travel from the current station to the next one. There is a special station at city $1$ which lets travellers instantaneously teleport to any other station that currently has a train. Teleportation and getting on a train once in the city both take $0$ minutes and all trains start at time $0$.

There are $M$ travellers at city $1$, and the $i$-th traveller has destination city $B_{i}$. They ask Chef to guide them to teleport to a particular station from which they can catch a train to go to their destination in the least time possible. In case it's not possible for a person to reach his destination, print $-1$.

Note: The input and output of this problem are large, so prefer using fast input/output methods.

------ Input ------

The first line contains an integer $T$, the number of test cases. Then the test cases follow.
Each test case contains three lines of input.
The first line contains two integers $N$, $M$.
The second line contains $N$ integers $A_{1}, A_{2}, \ldots, A_{N}$.
The third line contains $M$ integers $B_{1}, B_{2}, \ldots, B_{M}$.

------ Output ------
For each test case, output $M$ space-separated integers $C_{1}, C_{2}, \ldots, C_{M}$, where $C_{i}$ is the minimum time required by the $i$-th traveller to reach his destination and if the $i$-th traveller can't reach his destination, $C_{i} = -1$.

------ Constraints ------
$1 ≤ N, M ≤ 10^{5}$
$0 ≤ A_{i} ≤ 2$
$1 ≤ B_{i} ≤ N$
The sum of $N$ over all test cases is at most $10^{6}$.
The sum of $M$ over all test cases is at most $10^{6}$.

------ Subtasks ------
Subtask #1 (100 points): original constraints

----- Sample Input 1 ------
3

5 1

1 0 0 0 0

5

5 1

1 0 0 0 2

4

5 2

2 0 0 0 1

3 1
----- Sample Output 1 ------
4

1

-1 0
----- explanation 1 ------
Test Case $1$: The only person takes the train from station $1$ and hence takes $|5 - 1| = 4$ minutes to reach his destination.

Test Case $2$: The only person takes the train from station $5$ and hence takes $|5 - 4| = 1$ minute to reach his destination.

Test Case $3$: Since no train passes station $3$, it's impossible for the first person to reach his destination and since the second person is already at station $1$, it takes him $0$ minutes to reach his destination.

见题面

见题面