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)

#[allow(unused_macros)]
macro_rules! get {
    ([$t:ty] ; $n:expr) => {
        (0..$n)
        .map(|_| get!([$t])).collect::<Vec<_>>()
    };
    ($($t:ty),+ ; $n:expr) => {
        (0..$n).map(|_| get!($($t),+)).collect::<Vec<_>>()
    };
    ([$t:ty]) => {
        rl().split_whitespace()
        .map(|x| x.parse().unwrap())
        .collect::<Vec<$t>>()
    };
    ($t:ty) => {
        rl().parse::<$t>().unwrap()
    };
    ($($t:ty),*) => {
        {
            let line =rl();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap()),*)
        }
    };
}
fn rl() -> String {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    line.trim().to_string()
}

const MOD: usize = 1_000_000_007;

fn mod_pow(x: usize, n: usize, m: usize) -> usize {
    let mut ans = 1;
    let mut x = x;
    let mut n = n;
    while 0 < n {
        if n % 2 == 1 {
            ans = ans * x % m;
        }
        x = x * x % MOD;
        n >>= 1;
    }
    ans
}

fn ncr(n: usize, r: usize, m: usize) -> usize {
    let r = std::cmp::min(r, n - r);
    let mut nu = 1;
    let mut de = 1;
    for i in 0..r {
        nu = nu * (n - i) % m;
        de = de * (i + 1) % m;
    }
    nu * mod_pow(de, m - 2, m) % m
}
fn main() {
    let (n, a, b) = get!(usize, usize, usize);
    // eprintln!("{}, {}, {}", n, a, b);
    let x = mod_pow(2, n, MOD) - 1;
    let nca = ncr(n, a, MOD);
    let ncb = ncr(n, b, MOD);
    // eprintln!("{}, {}, {}", x, nca, ncb);
    let mut ans: i64 = (x as i64 - nca as i64 - ncb as i64) % MOD as i64;
    if ans < 0 {
        ans += MOD as i64;
    }
    println!("{}", ans);
}