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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
$input = file_get_contents('php://stdin');


$n = intval(explode(" ", $input)[0]);
$a = intval(explode(" ", $input)[1]);
$b = intval(explode(" ", $input)[2]);

$p = pow(10, 9) + 7;

function modpow($a, $exp, $mod)
{
  if ($exp == 0) return 1;
  if ($exp == 1) return $a % $mod;
  if ($exp % 2 == 0) {
    $d = modpow($a, $exp / 2, $mod);
    return ($d * $d) % $mod;
  }
  return (modpow($a, $exp - 1, $mod) * $a) % $mod;
}

$ret = modpow(2, $n, $p) - 1;

$upper = 1;
$lower = 1;
for ($i = 0; $i < $b; $i++) {
  $upper = ($upper * ($n - $i)) % $p;
  $lower = ($lower * ($i + 1)) % $p;
}
if ($lower % $p != 0) {
  $ret -= ($upper * modpow($lower, $p - 2, $p)) % $p;
}

$upper = 1;
$lower = 1;
for ($i = 0; $i < $a; $i++) {
  $upper = ($upper * ($n - $i)) % $p;
  $lower = ($lower * ($i + 1)) % $p;
}
if ($lower % $p != 0) {
  $ret -= ($upper * modpow($lower, $p - 2, $p)) % $p;
}

if ($ret < 0) $ret += $p;

echo $ret . PHP_EOL;