N Cities

In a country there are $N$ cities numbered from $1$ to $N$. To Travel along the cities there are total N bi directional roads. For each city numbered $i$ ($1 \le i < N$) there is a bi-directional road between city i and city $i+1$. Furthermore, there is a road between city $N$ and city $1$. People can only use any of these roads to travel from a city to another. As travel technology of this country is very advanced, it requires only 1 second time to travel from city $i$ to city $j$ if there is a road between these two cities. Now initially you will be given the address of $M$ people. That is, for every people $i$ you will be given an integer $a_i$, the city where $i^{th}$ person lives. Then There will be $Q$ queries. In each query you will be given an integer $X$. You will have to tell the total time that is required for all people to travel from their city to city $X$. Now as we know everyone hates long time travelling, they will take the shortest path to travel from their cities to city $X$.

Input

On the first line, there will be two integers $N$ ($3 ≤ N ≤ 10^9$) and $M$ ($1 ≤ M ≤ 2×10^5$) described in statement. Then the next $M$ line will contain one number each, $i^{th}$ of them will be $a_i$ ($1 ≤ a_i ≤ N$), the number of the city where $i^{th}$ person lives. Then there will be an integer $Q$ ($1 ≤ Q ≤ 10^5$), the number of queries. Then the following $Q$ lines will contain one integer $X$ ($1 ≤ X ≤ N$) each, the number (ID) of destination city described in statement.

Output

For each query print an integer, the total time that is required for all $M$ people to travel from their city to city $X$.

Sample

Input	Output
10 2 2 9 2 10 5	3 7