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.Diagnostics;
using System.Linq;
using System.Numerics;

internal static class CR
{
    public static string Get() { return Console.ReadLine(); }
    public static IEnumerable<string> GetTexts() { return Console.ReadLine().Split(' '); }
    public static int GetInteger() { return int.Parse(Console.ReadLine()); }
    public static IEnumerable<int> GetIntegers() { return Console.ReadLine().Split(' ').Select(x => int.Parse(x)); }
}

namespace AtCoder.D
{
    public class Program
    {
        public static int N { get; private set; }
        public static int A { get; private set; }
        public static int B { get; private set; }
        static BigInteger _up = 1;
        static BigInteger _down = 1;

        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var inputs = CR.GetIntegers().ToList();
            N = inputs[0];
            A = inputs[1];
            B = inputs[2];

            BigInteger count = 0;
            var mod = (BigInteger)Math.Pow(10, 9) + 7;
            for (int i = 1; i <= N; i++)
            {
                var cal = Calc_nCi(N, i);
                if (i == A || i == B) continue;

                count += cal;
                if (count > mod)
                {
                    count -= mod;
                }
            }

            return count % mod;
        }

        private static BigInteger Calc_nCi(int n, int i)
        {
            _up *= N - i + 1;
            _down *= i;

            return _up / _down;
        }
    }
}