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 Perl (v5.18.2) (judge verdict: Accepted)

use v5.18;
use warnings;

my ($n, $a, $b);
{
  my $in = <STDIN>;
  ($n, $a, $b) = split(" ", $in);
}
my $MOD = 1e9 + 7;
sub modpow {
  my ($a, $n, $MOD) = @_;
  my $res = 1;
  while ($n > 0) {
    $res = $res * $a % $MOD if $n & 1;
    $a = $a * $a % $MOD;
    $n >>= 1;
  }
  return $res;
}
sub modinv {
  my ($a, $MOD) = @_;
  return modpow($a, $MOD - 2, $MOD);
}
sub comb {
  my ($n, $k) = @_;
  my $a = 1;
  my $b = 1;
  for (my $i=0; $i<$k; $i++) {
    $a *= $n - $i;
    $a %= $MOD;
    $b *= $i + 1;
    $b %= $MOD;
  }
  $a * modinv($b, $MOD) % $MOD;
}

my $ans = modpow(2, $n, $MOD) - 1;
$ans += $MOD - comb($n, $a, $MOD);
$ans += $MOD - comb($n, $b, $MOD);
say $ans % $MOD;