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;
class Program
        {
            static void Main(string[] args)
            {
                string s = Console.ReadLine();
                var sa = s.Split(' ');
                long[] ia = new long[3];
                for (int i = 0; i < ia.Length; i++)
                {
                    ia[i] = int.Parse(sa[i]);
                }

                long total = 0;
                for(long l = ia[0];l > 0; l--)
                {
                    if(l != ia[1] && l!= ia[2])
                    {
                        long bunbo = 1;
                        long bunshi = 1;
                        long kaisuu = ia[0] - l;
                        for (long m = 0; m < kaisuu; m++)
                        {
                            bunbo *= ia[0] - m;
                            bunshi *= m + 1;
                        }
                        total += bunbo / bunshi;
                    }

                }
                total = total % ((long)(Math.Pow(10, 9)) + 7);

                Console.WriteLine(total);
            }
        }