Chocolate Bar

AtCoder

IDarc074_a

Time2000ms

Memory256MB

Difficulty—

There is a bar of chocolate with a height of $H$ blocks and a width of $W$ blocks. Snuke is dividing this bar into exactly three pieces. He can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle. Snuke is trying to divide the bar as evenly as possible. More specifically, he is trying to minimize $S_{max}$ - $S_{min}$, where $S_{max}$ is the area (the number of blocks contained) of the largest piece, and $S_{min}$ is the area of the smallest piece. Find the minimum possible value of $S_{max} - S_{min}$. ## Constraints * $2 ≤ H, W ≤ 10^5$ ## Input Input is given from Standard Input in the following format: $H$ $W$ [samples]

Samples

Input #1

3 5

Output #1

0

In the division below, $S_{max} - S_{min} = 5 - 5 = 0$.

![image](https://atcoder.jp/img/arc074/2a9b2ef47b750c0b7ba3e865d4fb4203.png)

Input #2

4 5

Output #2

2

In the division below, $S_{max} - S_{min} = 8 - 6 = 2$.

![image](https://atcoder.jp/img/arc074/a42aae7aaaadc4640ac5cdf88684d913.png)

Input #3

5 5

Output #3

4

In the division below, $S_{max} - S_{min} = 10 - 6 = 4$.

![image](https://atcoder.jp/img/arc074/eb0ad0cb3185b7ae418e21c472ff7f26.png)

Input #4

100000 2

Output #4

Input #5

100000 100000

Output #5

API Response (JSON)

{
  "problem": {
    "name": "Chocolate Bar",
    "description": {
      "content": "There is a bar of chocolate with a height of $H$ blocks and a width of $W$ blocks. Snuke is dividing this bar into exactly three pieces. He can only cut the bar along borders of blocks, and the shape ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc074_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a bar of chocolate with a height of $H$ blocks and a width of $W$ blocks. Snuke is dividing this bar into exactly three pieces. He can only cut the bar along borders of blocks, and the shape ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments