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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder.Abc
{
    class QuestionD
    {
        public struct nab
        {
            public int n;
            public int a;
            public int b;
        }

        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            // 整数配列の入力
            var x = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();

            var n = new nab() { n = x[0], a = x[1], b = x[2] };

            var sums = 0; 

            var sum = 1;
            var dep = 1;
            var a = 0;
            var b = 0;

            var isAdd = false;

            var min = (n.n + 1) / 2;

            if (n.n % 2 == 0) {
                isAdd = true;
            }

            for (int i = 1; i < min; i++) {
                dep *= i;
                sum *= n.n - i + 1;

                if (i == n.a || n.n - i == n.a) {
                    a = sum / dep;
                }

                if (i == n.b || n.n - i == n.b) {
                    b = sum / dep;
                }

                sums += sum / dep;
            }

            sums *= 2;

            sums += 1;

            if (isAdd) {
                dep *= min;
                sum *= n.n - min + 1;
                sums += sum / dep;
            }

            sums -= a + b;

            Console.WriteLine(sums % (Math.Pow(10, 9) + 7));

            Console.Out.Flush();
        }
    }
}