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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
import java.math.BigInteger;
public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        int a=sc.nextInt();
        int b=sc.nextInt();
        BigInteger ansb=pow(2,n);
        ansb=ansb.subtract(frac(n).divide(frac(a)).divide(frac(n-a)));
        ansb=ansb.subtract(frac(n).divide(frac(b)).divide(frac(n-b)));
        ansb=ansb.add(BigInteger.valueOf(-1));
        int ans=divq(ansb,1000000007);
        System.out.println(ans);
    }
    static long adjust(long a){
        long q=a/1000000007;
        return (a-q*1000000007);
    }
    static BigInteger frac(int a){
        BigInteger result=BigInteger.valueOf(1);
        for (int i=2;i<=a;i++){
            result=result.multiply(BigInteger.valueOf(i));
        }
        return result;
    }
        static BigInteger pow(int a,int b){
        BigInteger result=BigInteger.valueOf(1);
        for (int i=1;i<=b;i++){
            result=result.multiply(BigInteger.valueOf(a));
        }
        return result;
    }
    static int divq(BigInteger a,int b){
        BigInteger r=a.divide(BigInteger.valueOf(b));
        r=a.subtract(r.multiply(BigInteger.valueOf(b)));
        return r.intValue();
    }

}