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: Time Limit Exceeded)

#include <stdio.h>

long long int combi(int n, int r);

int main(void)
{
    long long int sum=0;
    int n,a,b,i;
    scanf("%d %d %d",&n,&a,&b);

    for(i=1; i<=n; i++){//n本の中から1本選ぶ場合・・・＞n本の中からn本選ぶ場合
        if((i!=a) && (i!=b)){
            sum += combi(n,i)%1000000007;
        }
    }

    printf("%lld\n",sum%1000000007);

    return 0;
}

long long int combi(int n, int r) {
    if (r == 0) {
        return 1;
    }
    
    return (n - r + 1) * combi(n, r - 1) / r;
}