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::str::FromStr;

fn get_one<T : FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    return s.trim().parse().ok().unwrap();
}

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

fn mod_pow(a : i64, b : i64, md : i64) -> i64 {
    if b == 0 { return 1; }
    if b % 2 == 0 {
        let h = mod_pow(a, b/2, md);
        return (h * h) % md;
    }
    else {
        return (a * mod_pow(a, b-1, md)) % md;
    }
}

fn mod_comb(a : i64,b : i64,md : i64) -> i64 {
    if a-b < b { return mod_comb(a,a-b,md); }
    let mut ans_mul = 1;
    let mut ans_div = 1;
    for i in 0..b {
        ans_mul *= a-i;
        ans_div *= i+1;
        ans_mul %= md;
        ans_div %= md;
    }
    return (ans_mul * mod_pow(ans_div, md-2, md)) % md;
}

fn main() {
    let v : Vec<i64> = get_vec();
    let n = v[0];
    let a = v[1];
    let b = v[2];
    let modn = 1000000007;
    let ans = (mod_pow(2,n,modn)-1 - mod_comb(n,a,modn) - mod_comb(n,b,modn)) % modn;
    println!("{}", (ans+modn)%modn);


}