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

namespace ConsoleApp5
{
    class Program
    {

        static void Main(string[] args)
        {
            String S = Console.ReadLine();
            String[] line = S.Split(' ');
            ulong n = ulong.Parse(line[0]);
            ulong a = ulong.Parse(line[1]);
            ulong b = ulong.Parse(line[2]);
            ulong ans = 0;

            ans = modpow(2, n) - 1;
            ans -= Combination(n, a);
            ans = ans % 1000000007;
            ans -= Combination(n, b);
            ans = ans % 1000000007;

            Console.WriteLine(ans);




        }
        public static ulong Combination(ulong n, ulong r)
        {
            if (n < 0 || r < 0 || r > n) throw new ArgumentException("不正な引数です．");

            if (n - r < r) r = n - r;
            if (r == 0) return 1;
            if (r == 1) return n;

            ulong[] numerator = new ulong[r];
            ulong[] denominator = new ulong[r];

            for (ulong k = 0; k < r; k++)
            {
                numerator[k] = n - r + k + 1;
                denominator[k] = k + 1;
            }

            for (ulong p = 2; p <= r; p++)
            {
                ulong pivot = denominator[p - 1];
                if (pivot > 1)
                {
                    ulong offset = (n - r) % p;
                    for (ulong k = p - 1; k < r; k += p)
                    {
                        numerator[k - offset] /= pivot;
                        denominator[k] /= pivot;
                    }
                }
            }

            ulong result = 1;
            for (ulong k = 0; k < r; k++)
            {
                if (numerator[k] > 1) result *= numerator[k];
            }

            return result;
        }

        public static ulong modpow(ulong a, ulong n)
        {//aのn乗を計算します。
            ulong res = 1;
            while (n > 0)
            {
                if (n % 2 == 1)
                {
                    res = res * a % 1000000007;
                }
                a = a * a % 1000000007;
                n >>= 1;
            }
            return res;
        }




    }
}