There are $N$ sprinklers in a field. Each sprinkler has some range up to where it can sprinkle water.
All the sprinklers are on the X-axis at coordinates $(X1,0),\ (X2,0),\ ..., (XN,0)$ and their respective ranges are $R1,\ R2,\ R3, ..., RN$ meaning that the $i^{th}$ sprinkler can sprinkle water from $[Xi-Ri,\ Xi+Ri]$ inclusive.
There is a big wall at 0 meaning that the water can not go another side irrespective of range.

You are asked $Q$ queries and in the $i^{th}$ query, you will be given an integer $K$. Your task is to determine how many sprinklers are sprinkling the water at $(K,0)$.
Assume, there is no sprinkler at $(0,0)$ and there is no query that has $K=0$.

Input format

• The first line contains an integer $T$ denoting the number of test cases.
• The first line of each test case contains two integers $N$ and $Q$ denoting the number of sprinklers and number of queries.
• The second line of each test case contains $N$ space-separated integers denoting the X-coordinates of the sprinklers.
• The third line of each test case contains $N$ space-separated integers denoting the range of the sprinklers.
• Next $Q$ line of each test case contains an integer $K$ for the query.

Output format

For each test case, print $Q$ lines denoting the number of sprinklers that sprinkle water at the position in the $i^{th}$ query.

Constraints

$1 \leq T \leq 10000$

$1 \leq N \leq 100000$

$1 \leq Q \leq N$

$1 \le |X_i| \le N$

$0 \leq R_i \leq N$

$-2N \leq K \leq 2N$

The sum of $N$ over all test cases do not exceed 100000.