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)

const MOD: u64 = 1000000007;

fn main() {
    let nab = read_vec::<u64>();
    let n = nab[0];
    let a = nab[1];
    let b = nab[2];

    let sum = (exp(2, n) + 2 * MOD - comb(n, a) - comb(n, b) - 1) % MOD;

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

fn exp(b: u64, n: u64) -> u64 {
    if n == 0 {
        return 1
    }

    if n % 2 == 0 {
        let tmp = exp(b, n/2);
        tmp * tmp % MOD
    } else {
        b * exp(b, n-1) % MOD
    }
}

fn comb(a: u64, b: u64) -> u64 {
    let b = {
        let tmp = a - b;
        if tmp < b { tmp } else { b }
    };

    let mut ch = 1;
    for i in 0..b {
        ch *= a - i;
        if ch > MOD {
            ch %= MOD;
        }
    }

    let mut mo = 1;
    let mut x = b;
    while x > 0 {
        mo *= x;
        if mo > MOD {
            mo %= MOD;
        }
        x -= 1;
    }

    ch * exp(mo, MOD-2) % MOD
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}