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: Accepted)

#include <stdio.h>
#include <stdlib.h>

long long div_mod(long long x, long long y, long long z)
{
	if (x % y == 0) return x / y;
	else return (div_mod((1 + x / y) * y - x, (z % y), y) * z + x) / y;
}

int main()
{
	long long n, a, b;
	scanf("%lld %lld %lld", &n, &a, &b);
	
	int i, j;
	long long m, total = 1, tmp[32] = {2}, ex[2] = {1, 1};
	for (i = 1; i < 32; i++) tmp[i] = tmp[i-1] * tmp[i-1] % 1000000007;
	for (i = 0, m = n; m > 0; i++, m = m >> 1) if (m % 2 == 1) total = total * tmp[i] % 1000000007;
	for (i = 0; i < a; i++) ex[0] = ex[0] * (n - i) % 1000000007;
	for (j = 1; j <= a; j++) ex[0] = div_mod(ex[0], j, 1000000007);
	for (ex[1] = ex[0]; i < b; i++) ex[1] = ex[1] * (n - i) % 1000000007;
	for (; j <= b; j++) ex[1] = div_mod(ex[1], j, 1000000007);
	
	printf("%lld\n", (total + 1000000007 * 2 - ex[0] - ex[1] - 1) % 1000000007);
	fflush(stdout);
	return 0;
}