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: Wrong Answer)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#[allow(unused_imports)]
use itertools::Itertools as _;
use proconio::input;
#[allow(unused_imports)]
use procontools::p;
#[allow(unused_imports)]
use std::cmp::*;

#[allow(non_upper_case_globals)]
const prime: u64 = 1_000_000_007;
use std::ops::*;
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub struct ModInt(u64);
impl ModInt {
    pub fn new(i: u64) -> Self {
        ModInt(i % prime)
    }
    pub fn inv(self) -> Self {
        debug_assert!(procontools::math::gcd(*self, prime) == 1);
        debug_assert!(*self != 0);
        self.pow(prime - 2)
    }
    pub fn pow(self, pow: u64) -> Self {
        let mut pow = pow;
        pow %= prime - 1;
        if pow == 0 {
            ModInt(1)
        } else if pow % 2 == 0 {
            let h = self.pow(pow >> 1);
            h * h
        } else {
            let h = self.pow(pow >> 1);
            h * h * self
        }
    }
}
impl Deref for ModInt {
    type Target = u64;
    fn deref(&self) -> &Self::Target {
        &self.0
    }
}
impl Add for ModInt {
    type Output = Self;
    fn add(self, other: Self) -> Self::Output {
        ModInt((*self + *other) % prime)
    }
}
impl Sub for ModInt {
    type Output = Self;
    fn sub(self, other: Self) -> Self::Output {
        if *self > *other {
            ModInt(*self - *other)
        } else {
            ModInt(*self + prime - *other)
        }
    }
}
impl Mul for ModInt {
    type Output = Self;
    fn mul(self, other: Self) -> Self::Output {
        ModInt(*self * *other % prime)
    }
}
impl Div for ModInt {
    type Output = Self;
    fn div(self, other: Self) -> Self::Output {
        self * other.inv()
    }
}
fn f(n: ModInt, k: ModInt) -> ModInt {
    (1..=k.0)
        .map(|i| (n - ModInt(i - 1)) / ModInt(i))
        .fold(ModInt(1), |p, x| p * x)
}

fn main() {
    input! {
        n:u64,a:u64,b:u64
    }
    let s = ModInt(2).pow(n) - ModInt(1);
    let ca = f(ModInt(n), ModInt(a));
    let cb = f(ModInt(n), ModInt(b));
    let ans = s - ca - cb;
    p!(ans.0);
}
*/

fn main() {
    let exe = "/tmp/binCFD83515";
    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>";