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.

Examples

Input

2 2
2 0
0 0
-1 0
1 0

Output

2
1

Input

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

Output

3
1
2

Input

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

Output

5
4
3
2
1

见题面

见题面