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: Time Limit Exceeded)

using System;
using static System.Console;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Diagnostics;

class Program
{
    private const int mod = 1000000007;

    static void Main()
    {
        var input = MyUtil.ReadintArray();
        var res = 0l;

        for (int i = 1; i <= input[0]; i++)
        {
            if (i == input[1] || i == input[2])
            {
                continue;
            }
            res += Combination(input[0], i);
            res %= mod;
        }

        WriteLine(res);
        ReadKey();
    }

    static long Combination(int a, int b)
    {
        long result = 1;
        for (int i = 0; i < b; i++)
        {
            result *= (a - i);
            result /= (i + 1);

            result %= mod;
        }
        return result;
    }
}


static class MyUtil
{
    /// <summary>
    /// 指定の桁のビットを取得します。
    /// </summary>
    /// <param name="num"></param>
    /// <param name="count">取得する桁。</param>
    /// <returns></returns>
    public static int GetBit(this int num, int count)
    {
        int mask = (int)Math.Pow(2, count - 1);
        return (num & mask) == 0 ? 0 : 1;
    }

    /// <summary>
    /// <c>int</c>を2進数ビット配列に変換します。
    /// </summary>
    /// <param name="num"></param>
    /// <returns></returns>
    public static int[] ToBitArray(this int num)
    {
        const int size = sizeof(int) * 8;
        var array = new int[size];
        for (int i = 0; i < size; i++)
        {
            array[i] = num.GetBit(size - i);
        }
        return array;
    }

    public static long[] ReadlongArray()
    {
        return ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
    }

    public static int[] ReadintArray()
    {
        return ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
    }

    /// <summary>
    /// <see cref="IEnumerable{T}"/>の各要素を並べてコンソールに出力します。各要素の間には半角スペースが一つ入ります。
    /// </summary>
    /// <typeparam name="T"></typeparam>
    /// <param name="ts"></param>
    public static void WriteToConsole<T>(this IEnumerable<T> ts)
    {
        StringBuilder stringBuilder = new StringBuilder();
        foreach (T t in ts)
        {
            stringBuilder.Append(t.ToString());
            stringBuilder.Append(" ");
        }
        stringBuilder.Remove(stringBuilder.Length - 1, 1);
        Console.WriteLine(stringBuilder.ToString());
    }

    public static void WriteToDebugConsole<T>(this IEnumerable<T> ts)
    {
        StringBuilder stringBuilder = new StringBuilder();
        foreach (T t in ts)
        {
            stringBuilder.Append(t.ToString());
            stringBuilder.Append(" ");
        }
        stringBuilder.Remove(stringBuilder.Length - 1, 1);
        System.Diagnostics.Debug.WriteLine(stringBuilder.ToString());
    }
}