Grid Coloring

AtCoder

IDarc080_b

Time2000ms

Memory256MB

Difficulty—

We have a grid with $H$ rows and $W$ columns of squares. Snuke is painting these squares in colors $1$, $2$, $...$, $N$. Here, the following conditions should be satisfied: * For each $i$ ($1 ≤ i ≤ N$), there are exactly $a_i$ squares painted in Color $i$. Here, $a_1 + a_2 + ... + a_N = H W$. * For each $i$ ($1 ≤ i ≤ N$), the squares painted in Color $i$ are _4-connected_. That is, every square painted in Color $i$ can be reached from every square painted in Color $i$ by repeatedly traveling to a horizontally or vertically adjacent square painted in Color $i$. Find a way to paint the squares so that the conditions are satisfied. It can be shown that a solution always exists. ## Constraints * $1 ≤ H, W ≤ 100$ * $1 ≤ N ≤ H W$ * $a_i ≥ 1$ * $a_1 + a_2 + ... + a_N = H W$ ## Input Input is given from Standard Input in the following format: $H$ $W$ $N$ $a_1$ $a_2$ $...$ $a_N$ [samples]

Samples

Input #1

2 2
3
2 1 1

Output #1

1 1
2 3

Below is an example of an invalid solution:

1 2
3 1

This is because the squares painted in Color $1$ are not 4-connected.

Input #2

3 5
5
1 2 3 4 5

Output #2

1 4 4 4 3
2 5 4 5 3
2 5 5 5 3

Input #3

1 1
1
1

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Grid Coloring",
    "description": {
      "content": "We have a grid with $H$ rows and $W$ columns of squares. Snuke is painting these squares in colors $1$, $2$, $...$, $N$. Here, the following conditions should be satisfied: *   For each $i$ ($1 ≤ i ≤",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc080_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a grid with $H$ rows and $W$ columns of squares. Snuke is painting these squares in colors $1$, $2$, $...$, $N$. Here, the following conditions should be satisfied:\n\n*   For each $i$ ($1 ≤ i ≤...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments