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)

use std::io::*;
use std::str::FromStr;

const MODULO: i64 = 1_000_000_000 + 7;
pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

pub fn read_n<T: FromStr>(n: usize) -> Vec<T> {
    read_n_logic::<T>(n, vec![])
}

pub fn read_n_logic<T: FromStr>(n: usize, mut a: Vec<T>) -> Vec<T> {
    match n {
        0 => a,
        _ => {
            a.push(read::<T>());
            read_n_logic(n - 1, a)
        }
    }
}
use std::cmp::{max, min};

pub fn ncr(a: i64, mut b: i64) -> i64 {
    let mut ret = 1;
    for i in 0..b {
        ret = ret * (a - i) % MODULO;
    }
    return ret * inverse(fact(b)) % MODULO;
}

fn inverse(x: i64) -> i64 {
    powmod(x, MODULO - 2)
}

fn fact(x: i64) -> i64 {
    let mut ret: i64 = 1;
    for i in 1..x + 1 {
        ret = ret * i % MODULO;
    }
    return ret;
}

fn powmod(x: i64, n: i64) -> i64 {
    if n == 0 {
        return 1;
    }
    if n % 2 == 0 {
        let k = powmod(x, n / 2);
        return (k * k) % MODULO;
    } else {
        let k = powmod(x, n / 2);
        return (((k * k) % MODULO) * x) % MODULO;
    }
}

fn main() {
    let n: i64 = read();
    let a: i64 = read();
    let b: i64 = read();
    let mut ans = 2;
    let mut cnt = 2;

    ans = (powmod(2 as i64, n) - 1 - ncr(n, a) - ncr(n, b) + MODULO) % MODULO;
    println!("{}", ans);
}