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 Rust (1.15.1) (judge verdict: Accepted)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|s| s.parse().ok().unwrap())
        .collect()
}

const MODULO: i64 = 1_000_000_000 + 7;
fn mod_pow(a: i64, n: i64, p: i64) -> i64 {
    if n == 0 {
        1
    } else if n % 2 == 0 {
        let x = mod_pow(a, n / 2, p);
        x * x % p
    } else {
        let x = mod_pow(a, n / 2, p);
        a * ((x * x) % p) % p
    }
}

fn combination(n: i64, r: i64, p: i64) -> i64 {
    let mut x = 1;
     for i in 0..r {
         x = x * (n - i) % p;
    }
    let mut y = 1;
    for i in 1..r+1 {
        y = y * i % p;
    }
    x * mod_pow(y, p - 2, p) % p
}

fn main() {
    let input = read_vec::<i64>();
    let n = input[0];
    let a = input[1];
    let b = input[2];

    let all = mod_pow(2, n, MODULO) - 1;

    let ans = ((all - combination(n, a, MODULO) + MODULO) % MODULO - combination(n, b, MODULO) + MODULO) % MODULO;


    println!("{}", ans);
}