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)

const MOD: usize = 1000000007;

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

    let mut ans = 0;
    for i in 1..1 << n {
        let x = (i as u64).count_ones();
        if x != a as u32 && x != b as u32 {
            ans += 1;
            ans %= MOD;
        }
    }
    println!("{}", ans);
}

// implementation of combination with mod
// ref: https://qiita.com/ofutonfuton/items/92b1a6f4a7775f00b6ae
fn mod_power(x: usize, n: usize) -> usize {
    let mut ret = 1;
    let mut xx = x;
    let mut nn = n;
    while nn > 0 {
        if nn & 1 > 0 {
            ret = ret * xx % MOD;
        }
        xx = xx * xx % MOD;
        nn = nn >> 1;
    }
    ret
}

fn combinations(n: usize, k: usize) -> usize {
    if n == 0 && k == 0 {
        return 1;
    }
    if n < k {
        return 0;
    }

    let mut fac = vec![1usize; n + 1];
    let mut ifac = vec![1usize; n + 1];
    for i in 0..n {
        fac[i + 1] = fac[i] * (i + 1) % MOD;
        ifac[i + 1] = ifac[i] * mod_power(i + 1, MOD - 2) % MOD;
    }
    let tmp = ifac[n - k] * ifac[k] % MOD;
    tmp * fac[n] % MOD
}

#[allow(dead_code)]
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}
#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}
#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}
#[allow(dead_code)]
fn yn(result: bool) {
    if result {
        println!("Yes");
    } else {
        println!("No");
    }
}