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;
use std::fmt::Debug;
use std::cmp;
#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn pow(x: i64, n: i64, mm: i64) -> i64{
    let mut ans = 1;
    let mut b = x;
    for i in 0..63{
        if (n >> i) & 1 == 1{
            ans *= b;
            ans %= mm;
        }
        b = b*b;
        b %= mm;
    }

    return ans;
}

fn main(){
    let line = read_as_vec::<i64>();
    let n = line[0];
    let mm = 1_000_000_007;
    let mut cn = pow(2, n, mm) - 1;
    for i in 1..3{
        let a = line[i];
        let mut x = 1;
        for i in n-a+1..n+1{
            x *= i;
            x %= mm;
        }
        let mut y = 1;
        for i in 1..a+1{
            y *= i;
            y %= mm;
        }
        let w = pow(y, mm-2, mm);
        cn -= (x*w)%mm;
    }

    while cn < 0{
        cn += mm;
    }

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