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)

pub 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()
}

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

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

const R: u64 = 1000000007;

fn pow(n: u64, r: u64) -> u64 {
    let mut ret = 1;
    if r > 0 {
        ret = pow(n, r / 2);
        ret = ret * ret % R;
        if r % 2 == 1 {
            ret = ret * n % R;
        }
    }
    ret
}

fn main() {
    let nab: Vec<u64> = read_vec();
    let n = nab[0];
    let a = nab[1];
    let b = nab[2];

    let mut ans = pow(2, n) - 1;

    let mut t1 = 1;
    for i in n - a + 1..n + 1 {
        t1 = (t1 * i) % R;
    }
    for i in 1..a + 1 {
        t1 = (t1 * pow(i, R - 2)) % R;
    }

    let mut t2 = 1;
    for i in n - b + 1..n + 1 {
        t2 = (t2 * i) % R;
    }
    for i in 1..b + 1 {
        t2 = (t2 * pow(i, R - 2)) % R;
    }

    ans = (ans + 2 * R - t1 - t2) % R;

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