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: Runtime Error)

use std::io;
use std::vec::Vec;
fn main() {
    let mut l1 = String::new();
    let mut l2 = String::new();
    let stdin = io::stdin();
    stdin.read_line(&mut l1).unwrap();
    stdin.read_line(&mut l2).unwrap();
    let trimed = l1.trim_right();
    let n = trimed.parse::<usize>().unwrap();
    let mut v: std::vec::Vec<i32> = Vec::with_capacity(n);

    let mut iter = l2.split_whitespace();
    for i in &mut iter {
        let num: i32 = i.parse().unwrap();
        v.push(num);
    }
    v.sort();
    let mut ans = 0;
    for a in 0..101 {
        let mut result = 0;
        for i in &v {
            result = result + ((a - i) * (a - i));
        }

        if a == 0 {
            ans = result
        } else {
            if ans > result {
                ans = result;
            }
        }
    }
    println!("{}", ans);
}