Multiple of Nine

AtCoder

IDwtf19_b

Time4000ms

Memory256MB

Difficulty—

Count the number of strings $S$ that satisfy the following constraints, modulo $10^9 + 7$. * The length of $S$ is exactly $N$. * $S$ consists of digits (`0`...`9`). * You are given $Q$ intervals. For each $i (1 \leq i \leq Q)$, the integer represented by $S[l_i \ldots r_i]$ (the substring of $S$ between the $l_i$\-th ($1$\-based) character and the $r_i$\-th character, inclusive) must be a multiple of $9$. Here, the string $S$ and its substrings may have leading zeroes. For example, `002019` represents the integer $2019$. ## Constraints * $1 \leq N \leq 10^9$ * $1 \leq Q \leq 15$ * $1 \leq l_i \leq r_i \leq N$ ## Input Input is given from Standard Input in the following format: $N$ $Q$ $l_1$ $r_1$ $:$ $l_Q$ $r_Q$ [samples]

Samples

Input #1

Output #1

136

For example, $S = $ `9072` satisfies the conditions because both $S[1 \ldots 2] = $ `90` and $S[2 \ldots 4] = $ `072` represent multiples of $9$.

Input #2

Output #2

Input #3

Output #3

862268030

API Response (JSON)

{
  "problem": {
    "name": "Multiple of Nine",
    "description": {
      "content": "Count the number of strings $S$ that satisfy the following constraints, modulo $10^9 + 7$. *   The length of $S$ is exactly $N$. *   $S$ consists of digits (`0`...`9`). *   You are given $Q$ interval",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "wtf19_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Count the number of strings $S$ that satisfy the following constraints, modulo $10^9 + 7$.\n\n*   The length of $S$ is exactly $N$.\n*   $S$ consists of digits (`0`...`9`).\n*   You are given $Q$ interval...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments