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::input;

#[derive(Debug, Copy, Clone, Eq, PartialEq)]
pub struct ModI64(i64);

const MODP: i64 = 1_000_000_007;

impl ModI64 {
    pub fn inv(self) -> Self {
        self.pow(MODP as u32 - 2)
    }

    pub fn new(x: i64) -> Self {
        Self(x % MODP)
    }

    pub fn pow(self, exp: u32) -> Self {
        let mut b: ModI64 = self;
        let mut a: ModI64 = 1i64.into();
        let mut x = exp;
        while x > 1 {
            if x & 1 == 1 {
                a = a * b;
            }
            x = x / 2;
            b = b * b;
        }
        if x == 1 {
            a = a * b;
        }
        a
    }
}

impl From<i64> for ModI64 {
    fn from(x: i64) -> Self {
        ModI64::new(x)
    }
}

impl std::fmt::Display for ModI64 {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl std::ops::Add<ModI64> for ModI64 {
    type Output = ModI64;

    fn add(self, rhs: ModI64) -> Self::Output {
        (self.0 + rhs.0).into()
    }
}

impl std::ops::Sub<ModI64> for ModI64 {
    type Output = ModI64;

    fn sub(self, rhs: ModI64) -> Self::Output {
        let x = self.0 - rhs.0;
        (if x.is_negative() { MODP + x } else { x }).into()
    }
}

impl std::ops::Mul<ModI64> for ModI64 {
    type Output = ModI64;

    fn mul(self, rhs: ModI64) -> Self::Output {
        (self.0 * rhs.0).into()
    }
}

impl std::ops::Div<ModI64> for ModI64 {
    type Output = ModI64;

    fn div(self, rhs: ModI64) -> Self::Output {
        self * rhs.inv()
    }
}

fn comb(n: i64, r: i64) -> ModI64 {
    let mut a = ModI64::new(1);
    for i in (n - r + 1)..=n {
        a = a * ModI64::new(i);
    }
    let mut b = ModI64::new(1);
    for i in 1..=r {
        b = b * ModI64::new(i);
    }
    a / b
}

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

    if n == 2 {
        println!("{}", 0);
    } else {
        let u = ModI64::new(2).pow(n as u32) - ModI64::new(1);
        let ans = u - comb(n as i64, a as i64) - comb(n as i64, b as i64);
        println!("{}", ans);
    }
}
*/

fn main() {
    let exe = "/tmp/binE2140D3C";
    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>";