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>

long double combination(long int a,long int b){
	  int i;
	  long double c = 1;
	  for (i = 0; i < b; i++) {
		     c *= a - i;
		     c /= i + 1;
	  }
	  return c;
}
int main(void){
    int n;
    long int a,b;
    scanf("%d %ld %ld",&n,&a,&b);
    long double sum;
    int i;
    for(i=0;i<n;i++){
        sum += combination(n,i);
    }
    sum = sum - combination(n,a) - combination(n,b);
    long int sum_a;
    sum_a = (long int)sum % 1000000007;
    printf("%ld\n",sum_a);
    return 0;
}