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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
class Ho{
  static long factorial(long n) {
      if (n > 0)
        return n * factorial(n - 1);
      else
        return 1;
    }
  static void Main(){
    var w = 1000000000+7;
    var zen = Console.ReadLine().Split();
    var n = long.Parse(zen[0]);
    var a = long.Parse(zen[1]);
    var b = long.Parse(zen[2]);
    long k = 0;
    for(var i = 1;i<= n;i++){
      if(i == a||i == b) continue;
      k += (factorial(n)/factorial(n-i))/factorial(i);
    }
    Console.WriteLine(k%w);
  }
}