Problem:
Score : 400 points

Problem Statement

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

Output

Print the number of bouquets that Akari can make, modulo (10^9 + 7). (If there are no such bouquets, print 0.)

Sample Input 1

4 1 3

Sample 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.

Sample Input 2

1000000000 141421 173205

Sample Output 2

34076506

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

Solution in OCaml (4.02.3) (judge verdict: Accepted)

let m = 1000000007
let n, a, b, dp = Scanf.scanf "%d %d %d" @@ fun n a b -> n, a, b, Array.make (max a b + 1) 0
let ( * ) a b = a * b mod m
let (-) a b = a - b + if a < b then m else 0
let rec f b n = if n <= 0 then 1 else let p = f b (n / 2) in p * p * if n mod 2 = 0 then 1 else b
let _ = dp.(0) <- 1; for i = 1 to max a b do dp.(i) <- dp.(i - 1) * (n - i + 1) * f i (m - 2) done; f 2 n - 1 - dp.(a) - dp.(b) |> Printf.printf "%d\n"