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)

use std::io::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

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

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: i64 = iterator.next().unwrap().parse().unwrap();
    let a: i64 = iterator.next().unwrap().parse().unwrap();
    let b: i64 = iterator.next().unwrap().parse().unwrap();

    let mut ans: i64 = pow(2, n);
    ans = (ans - 1) % MOD;
    ans = (ans - comb(n, a)) % MOD;
    ans = (ans - comb(n, b)) % MOD;
    if ans < 0 {
        ans += MOD;
    }

    return format!("{}", ans);
}

const MOD: i64 = 1000000007;

fn pow(n: i64, x: i64) -> i64 {
    if x == 0 {
        return 1;
    }

    return if x % 2 == 0 {
        let t = pow(n, x / 2);
        t * t % MOD
    } else {
        n * pow(n, x - 1) % MOD
    }
}

fn comb(n: i64, k: i64) -> i64 {
    let mut numerator: i64 = 1;
    let mut denominator: i64 = 1;
    for i in 0..k {
        numerator = numerator * (n - i) % MOD;
        denominator = denominator * (k - i) % MOD;
    }
    numerator * pow(denominator, MOD - 2) % MOD
}