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 (1.42.0) (judge verdict: Accepted)

use proconio::input;

static MOD: i64 = 1000000007;
fn helper(n:i64, a: i64) -> i64 {
  let mut numerator = 1;
  let mut denominator = 1;
  for i in 0..a {
    numerator = numerator * (n-i) % MOD;
    denominator = denominator * (i + 1) % MOD;
  }
  return numerator * (mod_pow(denominator, MOD - 2) % MOD) % MOD;
}

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

fn main() {
  input! {
    n: i64,
    a: i64,
    b: i64,
  }
  let mut result = mod_pow(2, n);
  result = (result - 1) % MOD;
  result = (result + MOD - helper(n, a)) % MOD;
  result = (result + MOD - helper(n, b)) % MOD;
  
  println!("{}", result);
}