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 System.Collections.Generic;
using System.Linq;

namespace PaizaTest
{
    class Program
    {
        static void Main(string[] args)
        {
            var nab = Console.ReadLine().Split(' ').Select(int.Parse).ToList();
            var n = nab[0];
            var a = nab[1];
            var b = nab[2];

            // n本花を持っている
            // aとbの数にならない本数で花束が作れる

            var kindofFlower = 0;
            for (int i = 1; i <= n; i++)
            {
                if (i == a || i == b)
                {
                    continue;
                }
                kindofFlower += C(n, i);
                //Console.WriteLine($"i: {i}, kindofFlower: {kindofFlower}");
            }

            Console.WriteLine(kindofFlower);
        }

        static int C(int originNum, int selectNum)
        {
            if (originNum == selectNum)
            {
                return 1;
            }
            long originValue = 1;
            long selectValue = 1;
            for (int i = 0; i < selectNum; i++)
            {
                originValue *= originNum - i ;
                originValue = originValue % 100000007;
                selectValue *= (1 + i) ;
                selectValue = selectValue % 1000000007;
                //Console.WriteLine($"i: {i}, selectedValue: {selectValue}");
            }

            return (int)(originValue / selectValue);
        }
    }
}