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::io::{self, BufRead};

const MOD: i64 = 1_000_000_007;

fn main() {
    let stdin = io::stdin();
    let mut lines = stdin.lock().lines();
    let nab = lines.next().unwrap().unwrap();
    let mut nab = nab.split_whitespace();
    let n: i64 = nab.next().unwrap().parse().unwrap();
    let a: i64 = nab.next().unwrap().parse().unwrap();
    let b: i64 = nab.next().unwrap().parse().unwrap();

    let mut ans = pow_mod(2, n, MOD);
    ans -= comb_mod(n, a, MOD);
    ans -= comb_mod(n, b, MOD);
    ans -= 1;
    ans %= MOD;
    if ans < 0 {
        ans += MOD
    };

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

fn mul_mod(a: i64, b: i64, m: i64) -> i64 {
    ((a % m) * (b % m)) % m
}

fn div_mod(a: i64, b: i64, m: i64) -> i64 {
    let b_inv = pow_mod(b, m - 2, m);
    mul_mod(a, b_inv, m)
}

fn pow_mod(a: i64, b: i64, m: i64) -> i64 {
    let (mut a, mut b, mut result) = (a % m, b, 1);
    while b > 0 {
        if b % 2 == 1 {
            result = (result * a) % m;
        }
        a = (a * a) % m;
        b /= 2;
    }
    result
}

fn comb_mod(a: i64, b: i64, m: i64) -> i64 {
    let b = std::cmp::min(b, a - b);
    let num = (a - b + 1..a + 1).fold(1, |acc, x| mul_mod(acc, x, m));
    let den = (1..b + 1).fold(1, |acc, x| mul_mod(acc, x, m));
    div_mod(num, den, m)
}