Problem:
Score : 200 points

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

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad
type Coord = (Int, Int)

main:: IO ()
main = do
    [n,m] <- readLine <$> getLine
    s1s <- replicateM n getLine
    s2s <- replicateM m getLine
    let as = map readLine2 s1s
    let cs = map readLine2 s2s
    mapM_ print $ solve m cs as

solve :: Int -> [Coord] -> [Coord] -> [Int]
solve m cs = map (nearest m cs)

nearest :: Int -> [Coord] -> Coord -> Int
nearest m cs ab = fst $ foldl f (0,dmax) (zip [1..m] ds)
    where
        ds = [dist ab cd | cd <- cs]
        f (j',d') (j, d) = if d < d' then (j,d) else (j',d')
        dmax = 4 * 100000000

readLine :: String -> [Int]
readLine = map read . words

readLine2 :: String -> (Int,Int)
readLine2 = tuplify2 . map read . words

tuplify2 :: [a] -> (a,a)
tuplify2 (x:y:_) = (x,y)

dist :: Coord -> Coord -> Int
dist (x1,y1) (x2,y2) = abs (x1-x2) + abs (y1-y2)