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::collections::HashSet;

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

    let mut set = HashSet::new();
    set.insert(a);
    set.insert(b);

    let result=  (0..n)
        .into_iter()
        .filter(|i| !set.contains(i))
        .map(|i| i % (10u64.pow(9) + 7))
        .map(|i| count_combinations(n, i))
        .fold(0, |acc, i| acc + i);

    print!("{}", result);
}

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()
}

#[inline]
fn count_combinations(n: u64, i: u64) -> u64 {
    (1..i + 1)
        .into_iter()
        .fold(1, |acc, i| (acc / i) * (n - (i -1)))
}