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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

#define MD 1000000007

long long power(long long a, long long b) {
	long long p;

	if (b == 0)
		return 1;
	p = power(a, b / 2);
	p = (long long) p * p % MD;
	if (b % 2)
		p = (long long) p * a % MD;
	return p;
}

long long choose(long long n, long long k) {
	return k == 0 ? 1 : (long long) choose(n - 1, k - 1) * n % MD * power(k, MD - 2) % MD;
}

int main() {
	long long n, a, b, ans;

	scanf("%lld%lld%lld", &n, &a, &b);
	ans = power(2, n) - 1 - choose(n, a) - choose(n, b);
	if (ans < 0)
		ans += MD;
	printf("%lld\n", ans);
	return 0;
}