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)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

fn mod_pow(n: i64, p: i64, m: i64) -> i64 {
    if p == 0 {
        1
    } else if p % 2 == 0 {
        let pow = mod_pow(n, p / 2, m) % m;
        pow * pow % m
    } else {
        let pow = mod_pow(n, p - 1, m);
        n * pow % m
    }
}

fn calc_remove(n: i64, a: i64, mod_num: i64) -> i64 {
    let mut x = 1;
    for i in (n + 1 - a)..(n + 1) {
        x = x * i % mod_num
    }

    let mut y: usize = 1;
    for i in 1..(a + 1) as usize {
        y = y * i % mod_num as usize
    }

    let y_pow = mod_pow(y as i64, mod_num - 2, mod_num);

    x * y_pow % mod_num
}

fn main() {
    input! {
        n: i64,
        a: i64,
        b: i64,
    }

    let mod_num = 1_000_000_007;

    let ans = mod_pow(2, n as i64, mod_num) - 1;

    let a_del = calc_remove(n, a, mod_num);

    let b_del = calc_remove(n, b, mod_num);

    let ans = ans - a_del - b_del;
    let ans = {
        let mut ret = ans;
        while ret < 0 {
            ret = ret + mod_num
        }
        ret % mod_num
    };

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