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 num::bigint::{ToBigInt as _, ToBigUint as _};
use num::pow::Pow as _;
use num::rational::Ratio;
use num::traits::{CheckedNeg as _, CheckedRem as _, Inv as _};
use num::{
    BigInt, BigUint, CheckedAdd as _, CheckedDiv as _, CheckedMul as _, CheckedSub as _,
    FromPrimitive as _, Num as _, One as _, ToPrimitive as _, Zero as _,
};
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[modtype::use_modtype]
type F = modtype::F<1_000_000_007u64>;

fn binomial(n: u64, r: u64) -> F {
    let mut res = F(1);
    let mut res_inv = F(1);
    for i in 0..r {
        res *= F(n - i);
        res_inv *= F(i + 1);
    }
    res * res_inv.inv()
}

fn main() {
    input! {
        n : u64,
        a : u64, b : u64,
    }

    if n == 2 {
        println!("0");
        return;
    }

    println!(
        "{}",
        F(2u64).pow(n) - F(1u64) - binomial(n, a) - binomial(n, b)
    );
}
*/

fn main() {
    let exe = "/tmp/binB182B0BD";
    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>";