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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;

namespace AtCoderPractice0704
{
    class MainClass
    {
        public static void Main(string[] args)
        {
          
            long[] nab = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            double n = nab[0] % (Math.Pow(10, 9) + 7);
            long a = nab[1];
            long b = nab[2];
            double ans = 0;


            //選ぶ本数selected
            for (double selected =1; selected <= n; selected++)
            {
                if (selected == a || selected == b) { continue; }

                ans += nCk(n, selected) ;

            }
            Console.WriteLine(ans);
        }

        public static double nCk(double n, double k)
        {
            if (n < k) return 0;
            if (n == k) return 1;
            double mod = Math.Pow(10, 9) + 7;
            double x = 1;
            for (double i = 0; i < k; i++)
            {
                x = x * (n - i) / (i + 1) ;
                x %= mod;
            }
            return x;
        }
    }
}