Checkpoints

AtCoder

IDabc057_b

Time2000ms

Memory256MB

Difficulty—

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

Samples

Input #1

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 $1$.

Input #2

Output #2

3
1
2

There can be multiple checkpoints at the same coordinates.

Input #3

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

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Checkpoints",
    "description": {
      "content": "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 ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc057_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ students and $M$ checkpoints on the $xy$\\-plane.  \nThe 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 ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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