Otoshidama

AtCoder

IDabc085_c

Time2000ms

Memory256MB

Difficulty—

The commonly used bills in Japan are $10000$\-yen, $5000$\-yen and $1000$\-yen bills. Below, the word "bill" refers to only these. According to Aohashi, he received an otoshidama (New Year money gift) envelope from his grandfather that contained $N$ bills for a total of $Y$ yen, but he may be lying. Determine whether such a situation is possible, and if it is, find a possible set of bills contained in the envelope. Assume that his grandfather is rich enough, and the envelope was large enough. ## Constraints * $1 ≤ N ≤ 2000$ * $1000 ≤ Y ≤ 2 × 10^7$ * $N$ is an integer. * $Y$ is a multiple of $1000$. ## Input Input is given from Standard Input in the following format: $N$ $Y$ [samples]

Samples

Input #1

9 45000

Output #1

4 0 5

If the envelope contained $4$ $10000$\-yen bills and $5$ $1000$\-yen bills, he had $9$ bills and $45000$ yen in total. It is also possible that the envelope contained $9$ $5000$\-yen bills, so the output `0 9 0` is also correct.

Input #2

20 196000

Output #2

\-1 -1 -1

When the envelope contained $20$ bills in total, the total value would be $200000$ yen if all the bills were $10000$\-yen bills, and would be at most $195000$ yen otherwise, so it would never be $196000$ yen.

Input #3

1000 1234000

Output #3

14 27 959

There are also many other possibilities.

Input #4

2000 20000000

Output #4

2000 0 0

API Response (JSON)

{
  "problem": {
    "name": "Otoshidama",
    "description": {
      "content": "The commonly used bills in Japan are $10000$\\-yen, $5000$\\-yen and $1000$\\-yen bills. Below, the word \"bill\" refers to only these. According to Aohashi, he received an otoshidama (New Year money gift)",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc085_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The commonly used bills in Japan are $10000$\\-yen, $5000$\\-yen and $1000$\\-yen bills. Below, the word \"bill\" refers to only these.\nAccording to Aohashi, he received an otoshidama (New Year money gift)...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments