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 competitive::prelude::*;

use std::ops::{Add, Div, Mul, Sub};


#[derive(Clone, Copy, Debug)]
pub struct ModInt<T: Copy + Clone + Add + Mul + Sub>(pub T);

type Num = usize;

const MOD: usize = 1e9 as usize + 7;

impl Add<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn add(self, other: ModInt<Num>) -> ModInt<Num> { ModInt::new(self.0 + other.0) }
}

impl Sub<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn sub(self, other: ModInt<Num>) -> ModInt<Num> { ModInt::new(self.0 + MOD - other.0) }
}

impl Mul<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn mul(self, other: ModInt<Num>) -> ModInt<Num> { ModInt::new(self.0 * other.0) }
}

impl Div<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn div(self, other: ModInt<Num>) -> ModInt<Num> { self * other.pow((MOD - 2) as usize) }
}

impl From<i32> for ModInt<Num> {
    fn from(item: i32) -> Self { ModInt::new(item as Num) }
}

fn pow_helper<T: Copy + Mul<Output=T>>(a: T, n: usize, memo: T) -> T {
    if n == 0 {
        memo
    } else if n & 1 == 1 {
        pow_helper(a * a, n >> 1, memo * a)
    } else {
        pow_helper(a * a, n >> 1, memo)
    }
}

impl ModInt<Num> {
    pub fn new(x: Num) -> Self { ModInt(x % MOD) }
    pub fn pow(self, e: usize) -> ModInt<Num> {
        pow_helper(self, e, ModInt(1))
    }
}

fn main() {
    input! {
        n: usize,
        a: usize,
        b: usize,
}
    // binomials[k] = nCk (1, n, n  * (n - 1) / 2, ...)
    let mut binomials = vec![ModInt::new(1); b + 1];
    for k in 1..=b {
        binomials[k] = binomials[k - 1] * ModInt::new(n - k + 1) / ModInt::new(k);
    }

    // 2 ^ n - nCa - nCb - 1
    let ans = (ModInt::new(2).pow(n) - binomials[a] - binomials[b]).0 - 1;
    println!("{}", ans);
}
*/

fn main() {
    let exe = "/tmp/bin242BB62F";
    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>";