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: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

using E = System.Linq.Enumerable;

public class Program
{
    const long Mod = (long)1e9 + 7;

    public static void Main()
    {
        var nab = Console.ReadLine().Split().Select(x => long.Parse(x)).ToArray();
        var n = nab[0];
        var a = nab[1];
        var b = nab[2];

        var k = Power(Mod, 2, n) - 1;
        var ca = Combination(Mod, n, a);
        var cb = Combination(Mod, n, b);
        k -= ca + cb - Mod * 2;
        k %= Mod;

        Console.WriteLine(k);
    }

    static long Power(long m, long n, long a)
    {
        var x = 1L;
        while (a > 0)
        {
            if ((a & 1) > 0)
            {
                x *= n; x %= m;
            }
            n *= n; n %= m;
            a >>= 1;
        }
        return x;
    }

    static long Combination(long m, long n, long k)
    {
        k = Math.Min(k, n - k);
        var x = 1L;
        var d = 1L;
        while (k > 0)
        {
            x *= n--; x %= m;
            d *= k--; d %= m;
        }
        return x * Inverse(m, d) % m;
    }

    static long Inverse(long m, long a)
    {
        long b = m;
        long x = 1, y = 0;
        long u = 0, v = 1;
        while (b > 0)
        {
            var k = a / b;
            Trans(out a, ref b, a - k * b);
            Trans(out x, ref u, x - k * u);
            Trans(out y, ref v, y - k * v);
        }
        return x < 0 ? x + m : x;
    }

    static void Trans(out long x, ref long y, long t)
    {
        x = y;
        y = t;
    }
}