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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::{fastout, input};

const M: i128 = 1_000_000_007;

fn modinv(mut x: i128, m: i128) -> i128 {
    let mut y = m;
    let mut u = 1;
    let mut v = 0;

    while y != 0 {
        let t = x / y;
        x -= t * y;
        u -= t * v;

        std::mem::swap(&mut x, &mut y);
        std::mem::swap(&mut u, &mut v);
    }

    (u + m) % m
}

fn modpow(mut x: i128, mut p: i128, m: i128) -> i128 {
    let mut r = 1;
    while p != 0 {
        if p % 2 == 1 {
            r = (r * x) % m;
        }
        x = (x * x) % m;
        p /= 2;
    }
    r
}

#[fastout]
fn main() {
    input! {in_n: i128, in_a: i128, in_b: i128};
    let mut f0 = 1;
    let mut f1 = 1;
    let mut ca = 0;

    for i in 1..=in_b {
        f0 = (f0 * (in_n - i + 1)) % M;
        f1 = (f1 * i) % M;

        if i == in_a {
            ca = (f0 * modinv(f1, M)) % M;
        }
    }

    let cb = (f0 * modinv(f1, M)) % M;
    let mut cnt = modpow(2, in_n, M);

    cnt = (cnt - 1 + M) % M;
    cnt = (cnt - ca + M) % M;
    cnt = (cnt - cb + M) % M;

    println!("{}", cnt);
}
*/

fn main() {
    let exe = "/tmp/bin7F340E9E";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";