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: Runtime Error)

import java.util.*;
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();
   int total = 0;
   int nKaijyou=1;
   
   for(int i=1;i<=n;i++)nKaijyou*=i;
   int Kaijyou1=1;
   int Kaijyou2=nKaijyou;
   for(int i=1;i<=n;i++){
     Kaijyou1*=i;
     Kaijyou2/=(n-i+1);
     if(i!=a && i!=b){
     int totalSub=nKaijyou;
     
     totalSub/=Kaijyou1;
     
     totalSub/=Kaijyou2;
     total+=totalSub;
     total=total%((int)Math.pow(10,9)+7);
     }
   }
   System.out.println(""+total);
 }
}