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

namespace ConsoleApp15
{
    class Class338
    {
        static void Main()
        {
            var r = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int n = r[0];
            int a = r[1];
            int b = r[2];

            long all = (long)Modular.Pow(2, n) - 1;
            long A = (long)Modular.Ncr(n, a);
            long B = (long)Modular.Ncr(n, b);
            long ans = all - A - B;
            while (ans < 0) ans += 1000000007;
            Console.WriteLine(ans);
        }
    }
    class Modular  //Modしながら計算するクラス
    {
        private const int M = 1000000007;
        private long value;
        public Modular(long value) { this.value = value; }
        public static implicit operator Modular(long a)
        {
            var m = a % M;
            return new Modular((m < 0) ? m + M : m);
        }
        public static Modular operator +(Modular a, Modular b)
        {
            return a.value + b.value;
        }
        public static Modular operator -(Modular a, Modular b)
        {
            return a.value - b.value;
        }
        public static Modular operator *(Modular a, Modular b)
        {
            return a.value * b.value;
        }
        public static Modular Pow(Modular a, int n)
        {
            switch (n)
            {
                case 0:
                    return 1;
                case 1:
                    return a;
                default:
                    var p = Pow(a, n / 2);
                    return p * p * Pow(a, n % 2);
            }
        }
        public static Modular operator /(Modular a, Modular b)
        {
            return a * Pow(b, M - 2);
        }
        private static readonly List<int> facs = new List<int> { 1 };
        public static Modular Fac(int n)   //階乗
        {
            for (int i = facs.Count; i <= n; ++i)
            {
                facs.Add((int)(Math.BigMul(facs.Last(), i) % M));
            }
            return facs[n];
        }
        public static Modular Fac(int r,int n)
        {
            int temp = 1;
            for(int i = r; i <= n; i++)
            {
                temp = (int)(Math.BigMul(temp, i) % M);
            }
            return temp;
        }
        public static Modular Ncr(int n, int r) //nCr
        {
            return (n < r) ? 0
                 : (n == r) ? 1
                            : (n < 1000000) ? Fac(n) / (Fac(r) * Fac(n - r))
                                : Fac(n-r+1, n) / Fac(r);
        }
        public static explicit operator int(Modular a)
        {
            return (int)a.value;
        }
    }
}