Checkpoints

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

inputFormat

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

outputFormat

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

样例

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

3
1
2

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