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;

class Program
{

    static long calc = 1;
    static long div = 1000000000 + 7;
    static void Main(string[] args)
    {
        var l1 = ReadLongArray();

        long N = l1[0];
        long a = l1[1];
        long b = l1[2];

        long numMax = Math.Min(N, 200000);
        var total = Math.Pow(2, N) -1;
        var minus = Math.Pow(2, N-a) - 1 + Math.Pow(2, N - b) - 1 ;

        var result = (total - minus) % div;

        Console.WriteLine(result);
    }

    static string[] ReadStringArray()
    {
        return Console.ReadLine().Trim().Split(' ');
    }

    static int[] ReadIntArray()
    {
        return ReadStringArray().Select(_ => int.Parse(_)).ToArray();
    }

    static long[] ReadLongArray()
    {
        return ReadStringArray().Select(_ => long.Parse(_)).ToArray();
    }
}