In the game Chess World, there are multiple kings and the location of each king on the board is known to you. In a single step, a king can move in one of directions:
For every query you need to solve, you are given a meeting point for the kings to meet and your task is to calculate the sum of the minimum number of steps for each king to reach the meeting point.
Input Format
The first line contains two space-separated integers, , denoting the number of kings and , denoting the number of queries.
The next lines describe the locations of the kings. In particular, the line two space-separated integers and denoting the coordinates of the location of the king.
The next lines describe the queries. In particular, the line contains two space-separated integers and denoting the coordinates of the meeting point in the query.
Constraints
Output Format
For each query, print the sum of the minimum number of steps for each king to reach the meeting point.
Sample Input 0
5 2
3 3
5 1
2 4
2 1
2 3
4 2
5 3
Sample Output 0
8
13
Explanation 0
Query 1:
- The king will take step to reach
- The king will take step to reach
- The king will take steps to reach
- The king will take steps to reach
- The king will take steps to reach
Hence, the answer is
Query 2:
- The king will take steps to reach
- The king will take steps to reach
- The king will take steps to reach
- The king will take steps to reach
- The king will take steps to reach
so the answer is