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)

const MOD: i64 = 1000000007;

fn modpow(a: i64, n: i64) -> i64 {
    let mut a = a;
    let mut n = n;
    let mut res = 1;
    while n > 0 {
        if n & 1 > 0 {
            res = res * a % MOD;
        }
        a = a * a % MOD;
        n >>= 1;
    }
    res
}

fn modinv(a: i64) -> i64 {
    let mut a = a;
    let mut b = MOD;
    let mut u = 1;
    let mut v = 0;
    while b > 0 {
        let t = a / b;
        a -= t * b;
        std::mem::swap(&mut a, &mut b);
        u -= t * v;
        std::mem::swap(&mut u, &mut v);
    }
    u %= MOD;
    if u < 0 {
        u += MOD;
    }
    u
}

fn main() {
    let (n, a, b): (i64, i64, i64) = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let mut ws = buf.split_whitespace();
        let n = ws.next().unwrap().parse().unwrap();
        let a = ws.next().unwrap().parse().unwrap();
        let b = ws.next().unwrap().parse().unwrap();
        (n, a, b)
    };
    let mut ans = modpow(2, n) - 1;

    let mut c = 1;
    for i in 1..(a + 1) {
        c *= n - i + 1;
        c %= MOD;
        c *= modinv(i);
        c %= MOD;
    }
    ans -= c;
    let mut c = 1;
    for i in 1..(b + 1) {
        c *= n - i + 1;
        c %= MOD;
        c *= modinv(i);
        c %= MOD;
    }
    ans -= c;
    ans += MOD * 2;
    ans = ans % MOD;
    println!("{}", ans);
}