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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

    class Program
    {
        static void Main(string[] args)
        {
            string input_line = System.Console.ReadLine();
            var split = input_line.Split(' ');
            var n = long.Parse(split[0]);
            var a = long.Parse(split[1]);
            var b = long.Parse(split[2]);
            var result = (long)Math.Pow(2,n) - combination(n,a) - combination(n,b);
            result--;
        //    System.Console.WriteLine(Factorial(a));
         //   System.Console.WriteLine(Factorial(b));
            System.Console.WriteLine(result);
         //   System.Console.ReadLine();
        }
        public static long Factorial(long n)
        {
            long k = n;
            long ret = 1;
            if (n == 1) return n;
            while(k > 1)
            {
                ret *= k;
                k--;
            }
            return ret;
        }
        public static long combination(long n, long k )
        {
            return Factorial(n) / Factorial(n - k) / Factorial(k);
        }
    }