Problem C
All Pair Sums

You are given two multisets of integers, $A$ and $B$. Then you are given queries containing a number $x$ and are asked to find the number of ways to write $x$ as a sum of two numbers $a\in A$ and $b\in B$.

Input

The first line of input contains two positive integers $n,m$, the number of values in each multiset. The next two lines then contain the integers in each multiset. Each value $x$ in the multisets satisfies $-{10}^5\le x\le {10}^5$. Next there is a line with a positive integer $q\le {10}^5$, the number of queries. Next there are $q$ lines, each containing an integer $x$ satisfying $-{10}^9\le x\le {10}^9$.

Output

For each query $x$ you should print the number of ways to pick $a\in A$ and $b\in B$ such that $x=a+b$. Print each number on its own line.

3 4
1 2 3
4 5 6 7
3
5
7
9

1
3
2