Bouquet

AtCoder

IDabc156_d

Time2000ms

Memory256MB

Difficulty—

Akari has $n$ kinds of flowers, one of each kind. She is going to choose one or more of these flowers to make a bouquet. However, she hates two numbers $a$ and $b$, so the number of flowers in the bouquet cannot be $a$ or $b$. How many different bouquets are there that Akari can make? Find the count modulo $(10^9 + 7)$. Here, two bouquets are considered different when there is a flower that is used in one of the bouquets but not in the other bouquet. ## Constraints * All values in input are integers. * $2 \leq n \leq 10^9$ * $1 \leq a < b \leq \textrm{min}(n, 2 \times 10^5)$ ## Input Input is given from Standard Input in the following format: $n$ $a$ $b$ [samples]

Samples

Input #1

4 1 3

Output #1

7

In this case, Akari can choose $2$ or $4$ flowers to make the bouquet.
There are $6$ ways to choose $2$ out of the $4$ flowers, and $1$ way to choose $4$, so there are a total of $7$ different bouquets that Akari can make.

Input #2

1000000000 141421 173205

Output #2

34076506

Print the count modulo $(10^9 + 7)$.

API Response (JSON)

{
  "problem": {
    "name": "Bouquet",
    "description": {
      "content": "Akari has $n$ kinds of flowers, one of each kind. She is going to choose one or more of these flowers to make a bouquet. However, she hates two numbers $a$ and $b$, so the number of flowers in the bou",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc156_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Akari has $n$ kinds of flowers, one of each kind.\nShe is going to choose one or more of these flowers to make a bouquet.\nHowever, she hates two numbers $a$ and $b$, so the number of flowers in the bou...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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