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

fn main() {
    let n: i64 = read();
    let a: i64 = read();
    let b: i64 = read();

    let all = pow(2, n) - 1;

    let combin_a = combination(n, a);
    let combin_b = combination(n, b);
    let ans = if all - combin_a - combin_b > 0 {
        all - combin_a - combin_b
    } else {
        (all + combin_a + combin_b) % PRIME
    };

    println!("{}", ans);
}

const PRIME: i64 = 1000000007;

fn pow(x: i64, n: i64) -> i64 {
    if n == 0 {
        1
    } else if n % 2 == 0 {
        pow(x * x, n / 2) % PRIME
    } else {
        pow(x, n - 1) % PRIME
    }
}

pub fn combination(n: i64, r: i64) -> i64 {
    let num = (2..r + 1).fold(1, |a, i| (a * i) % PRIME);
    let den = (n - r + 1..n + 1).fold(1, |a, i| (a * i) % PRIME);
    den * pow(num, PRIME - 2)
}

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|b| b.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}