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.Linq;
using System.Collections.Generic;


class Program
{
    private static List<long> Facs = new List<long> { 1 };
    static void Main(string[] args)
    {
        const long mod = 1000000007;

        // 入力
        long[] nab = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long n = nab[0];
        long a = nab[1];
        long b = nab[2];


        long ans = Mpow(2, n,mod)-1;
        ans = ans - (Ncr(n, a)%mod) - (Ncr(n, b)%mod);
        Console.WriteLine(ans);
    }
    static long Mpow(long x, long n, long m)
    {
        long ans = 1;
        while (n > 0)
        {
            if (n % 2 == 1)
            {
                ans = ans * x % m;
                n -= 1;
            }
            x = x * x % m;
            n /= 2;
        }
        return ans;
    }
    static long Ncr(long n, long r)
    {
        long ret = 1;
        for (int i = 1; i <= r; i++)
        {
            ret = ret * (n - i + 1) / i;
        }

        return ret;
    }
}