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: Time Limit Exceeded)

<?php
define('MOD', 1000000007);

function mul($a, $b) {
	return (($a % MOD) * ($b % MOD)) % MOD;
}

function power($a, $b) {
	global $memo;
	if ($b === 0) {
		return 1;
	} else if ($b === 1) {
		return $a;
	} else if ($b % 2 === 0) {
		$bb = $b / 2;
		$ret = pow(power($a, $bb) % MOD, 2);
		return $ret % MOD;
	} else {
		$bb = ($b - 1) / 2;
		$ret = pow(power($a, $bb) % MOD, 2) % MOD;
		$ret = $ret * $a;
		return $ret % MOD;
	}
}

function div($a, $b) {
	return mul($a, power($b, MOD - 2));
}

function nCr($n, $r) {
    $ret = 1;
    for ($i = $n; $i > $n - $r; $i--) {
        $ret = mul($ret, $i);
    }
    for ($i = $r; $i > 0; $i--) {
        $ret = div($ret, $i);
    }
    return $ret;
}

fscanf(STDIN, '%d %d %d', $n, $a, $b);
$nn = power(2, $n);
$aa = nCr($n, $a);
$bb = nCr($n, $b);
$ans = $nn - $aa - $bb - 1;
while($ans < 0) {
    $ans += MOD;
}
echo $ans;