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.Text;
using System.Collections.Generic;
using System.Linq;
using E = System.Linq.Enumerable;

class Program
{
    static void Main(string[] args)
    {
        //入力を受け取る
        var NAB = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        long N = NAB[0];
        long A = NAB[1];
        long B = NAB[2];
        //N個のものからR個選ぶ組み合わせ
        var kaijo = new long[B + 1];
        //階乗のモジュラー逆数
        var Ikaijo = new long[B + 1];
        var kaijon = new long[B + 1];
        kaijo[0] = 1;
        Ikaijo[0] = 1;
        kaijon[0] = N;
        long mo = 1000000007;
        for (long i = 1; i < B + 1; i++)
        {
            kaijo[i] = (kaijo[i - 1] * i) % 1000000007;
            Ikaijo[i] = RepeatSquaring(kaijo[i]);
            kaijon[i] = (kaijon[i - 1] * (N - i)) % mo;
        }


        //long ans = (((kaijo[N]%mo)*(Ikaijo[R]%mo)%mo)*Ikaijo[N-R])%mo;
        long ans = RepeatSquaring(2, N) - (1 + (kaijon[B-1] * Ikaijo[B])%mo + (kaijon[A-1] * Ikaijo[A])%mo)%mo;
           
        Console.WriteLine(ans);
    }


    //繰り返し2乗法
    static long RepeatSquaring(long N, long M = 1000000005, long mod = 1000000007)
    {
        if (M == 0)
        {
            return 1;
        }
        else if (M % 2 == 0)
        {
            long t = RepeatSquaring(N, (M / 2), mod) % mod;
            return (t * t) % mod;
        }
        else
        {
            return ((N % mod) * RepeatSquaring(N, M - 1, mod)) % mod;
        }
    }
}