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.IO;
using System.Collections.Generic;
using System.Linq;

namespace test
{
    class MainClass
    {


        public static long Factorial(int n) =>
            n == 0 ? 1L : n * Factorial(n - 1);

        public static long Combi(int n, int r)
        {
            long ans = 0;
            ans = Factorial(n) / (Factorial(n - r) * Factorial(r));
            return ans;
        }

        public static void Main(string[] args)
        { 
            string[] str = Console.ReadLine().Split(' ');
            
            long d = (long)Math.Pow(10, 9) + 7;
            int n = int.Parse(str[0]);
            int a = int.Parse(str[1]);
            int b = int.Parse(str[2]);
            long ans = 0;
            for(int i=0; i<n; i++)
            {
                if(i == a | i == b)
                {
                    continue;
                }
                ans += Combi(n, i);
            }
            ans = ans % d;

            Console.WriteLine(ans);
            
            


        }

    }

}