Iroha and Haiku

AtCoder

IDarc058_c

Time4000ms

Memory256MB

Difficulty—

_Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order._ Iroha is looking for _$X,Y,Z$\-Haiku_ (defined below) in integer sequences. Consider all integer sequences of length $N$ whose elements are between $1$ and $10$, inclusive. Out of those $10^N$ sequences, how many contain an $X,Y,Z$\-Haiku? Here, an integer sequence $a_0, a_1, ..., a_{N-1}$ is said to _contain an $X,Y,Z$\-Haiku_ if and only if there exist four indices $x, y, z, w (0 ≦ x < y < z < w ≦ N)$ such that all of the following are satisfied: * $a_x + a_{x+1} + ... + a_{y-1} = X$ * $a_y + a_{y+1} + ... + a_{z-1} = Y$ * $a_z + a_{z+1} + ... + a_{w-1} = Z$ Since the answer can be extremely large, print the number modulo $10^9+7$. ## Constraints * $3 ≦ N ≦ 40$ * $1 ≦ X ≦ 5$ * $1 ≦ Y ≦ 7$ * $1 ≦ Z ≦ 5$ ## Input The input is given from Standard Input in the following format: $N$ $X$ $Y$ $Z$ [samples]

Samples

Input #1

3 5 7 5

Output #1

1

Here, the only sequence that contains a $5,7,5$\-Haiku is $[5, 7, 5]$.

Input #2

4 5 7 5

Output #2

Input #3

37 4 2 3

Output #3

863912418

Input #4

40 5 7 5

Output #4

562805100

API Response (JSON)

{
  "problem": {
    "name": "Iroha and Haiku",
    "description": {
      "content": "_Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order._ Iroha is looking for _$X,Y,Z$\\-Haiku_ (defined below) in integer sequences. Cons",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc058_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "_Haiku is a short form of Japanese poetry. A Haiku consists of three phrases with 5, 7 and 5 syllables, in this order._\nIroha is looking for _$X,Y,Z$\\-Haiku_ (defined below) in integer sequences.\nCons...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments