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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
class test{
  static long mod =1000000007;
  public static void Main(){
    var nab =  Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList();
    long n = nab[0];
    long a = nab[1];
    long b = nab[2];
    long res = (Mul(2,n)-1)%mod;

    long A = Conv(n,a);
    long B = Conv(n,b);
    res = (res%mod)-(A%mod)-(B%mod);
    Console.WriteLine(res);
  }
  
  static long Mul(long x, long n){
    if(n==1){
      return x %mod;
    }else if(n%2 ==1 ){
      return (x * Mul(x,n-1)) %mod;
    }
    long z = Mul(x,n/2);
    return (z*z) %mod;
  }
  
  static long Conv(long n, long m){
    long x =1;
    long y =1;  
    m = Math.Min(m,n-m);
    while(m>0){
      x*=n--;
      x%=mod;
      y*=m--;
      y%=mod;
    }
    return x/y;
  }
}