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)

#![allow(non_snake_case)]
#![allow(dead_code)]
#![allow(unused_macros)]
#![allow(unused_imports)]

use std::cmp::*;
use std::collections::*;

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    }
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

macro_rules! chmax {
    ($x:expr, $e:expr) => {
        if $x < $e {
            $x = $e;
        }
    };
}
macro_rules! chmin {
    ($x:expr, $e:expr) => {
        if $x > $e {
            $x = $e;
        }
    };
}

macro_rules! debug {
    ($($a:expr),*) => {
        eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

const INF: i64 = 1 << 60;

use std::ops::*;

const MOD: usize = 1000000007;
#[derive(Copy, Clone)]
struct ModInt {
    n: usize,
}

impl ModInt {
    fn from_usize(n: usize) -> ModInt {
        ModInt { n: n }
    }
    fn pow(self, power: usize) -> ModInt {
        if power == 0 {
            return ModInt::from_usize(1);
        }
        if power % 2 == 0 {
            let t = self.pow(power/2);
            return t * t;
        }
        self * self.pow(power-1)
    }
    fn inv(self) -> ModInt {
        self.pow(MOD - 2)
    }
}

impl Add for ModInt {
    type Output = ModInt;

    fn add(self, rhs: ModInt) -> ModInt {
        let mut tmp = self;
        tmp.n += rhs.n;
        tmp.n %= MOD;
        tmp
    }
}

impl Sub for ModInt {
    type Output = ModInt;

    fn sub(self, rhs: ModInt) -> ModInt {
        let mut tmp = self;
        if tmp.n < rhs.n {
            tmp.n += MOD;
        }
        tmp.n -= rhs.n;
        tmp
    }
}

impl Mul for ModInt {
    type Output = ModInt;

    fn mul(self, rhs: ModInt) -> ModInt {
        let mut tmp = self;
        tmp.n *= rhs.n;
        tmp.n %= MOD;
        tmp
    }
}

impl Div for ModInt {
    type Output = ModInt;

    fn div(self, rhs: ModInt) -> ModInt {
        let mut tmp = self;
        tmp.n *= rhs.inv().n;
        tmp.n %= MOD;
        tmp
    }
}

fn fact(n: ModInt) -> ModInt {
    let mut res = ModInt::from_usize(1);
    for i in 1..(n.n+1) {
        res = res * ModInt::from_usize(i);
    }
    res
}

fn perm(n: ModInt, k: ModInt) -> ModInt {
    let mut res = ModInt::from_usize(1);
    for i in (n.n - k.n + 1)..(n.n+1) {
        res = res * ModInt::from_usize(i);
    }
    res
}

fn com(n: ModInt, k: ModInt) -> ModInt {
    perm(n, k) * fact(k).inv()
}

fn main() {
    input!{
        n: usize,
        a: usize,
        b: usize,
    }
    let n = ModInt::from_usize(n);
    let a = ModInt::from_usize(a);
    let b = ModInt::from_usize(b);
    let ans = ModInt::from_usize(2).pow(n.n)
        - com(n, a) - com(n, b) - ModInt::from_usize(1);
    println!("{}", ans.n);
}