100571: [AtCoder]ABC057 B - Checkpoints

Problem Statement

There are $N$ students and $M$ checkpoints on the $xy$-plane.
The coordinates of the $i$-th student $(1 \leq i \leq N)$ is $(a_i,b_i)$, and the coordinates of the checkpoint numbered $j$ $(1 \leq j \leq M)$ is $(c_j,d_j)$.
When the teacher gives a signal, each student has to go to the nearest checkpoint measured in Manhattan distance.
The Manhattan distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $|x_1-x_2|+|y_1-y_2|$.
Here, $|x|$ denotes the absolute value of $x$.
If there are multiple nearest checkpoints for a student, he/she will select the checkpoint with the smallest index.
Which checkpoint will each student go to?

Constraints

• $1 \leq N,M \leq 50$
• $-10^8 \leq a_i,b_i,c_j,d_j \leq 10^8$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$ $M$
$a_1$ $b_1$
$:$  
$a_N$ $b_N$
$c_1$ $d_1$
$:$  
$c_M$ $d_M$

Output

Print $N$ lines.
The $i$-th line $(1 \leq i \leq N)$ should contain the index of the checkpoint for the $i$-th student to go.

Sample Input 1

2 2
2 0
0 0
-1 0
1 0

Sample Output 1

2
1

The Manhattan distance between the first student and each checkpoint is:

• For checkpoint $1$: $|2-(-1)|+|0-0|=3$
• For checkpoint $2$: $|2-1|+|0-0|=1$

The nearest checkpoint is checkpoint $2$. Thus, the first line in the output should contain $2$.

The Manhattan distance between the second student and each checkpoint is:

• For checkpoint $1$: $|0-(-1)|+|0-0|=1$
• For checkpoint $2$: $|0-1|+|0-0|=1$

When there are multiple nearest checkpoints, the student will go to the checkpoint with the smallest index. Thus, the second line in the output should contain $1$.

Sample Input 2

3 4
10 10
-10 -10
3 3
1 2
2 3
3 5
3 5

Sample Output 2

3
1
2

There can be multiple checkpoints at the same coordinates.

Sample Input 3

5 5
-100000000 -100000000
-100000000 100000000
100000000 -100000000
100000000 100000000
0 0
0 0
100000000 100000000
100000000 -100000000
-100000000 100000000
-100000000 -100000000

Sample Output 3

5
4
3
2
1