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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
        }

        public void Solve(ConsoleInput cin)
        {
            var n = cin.ReadInt;
            var a = cin.ReadInt;
            var b = cin.ReadInt;

            var ans = ((ModInt)2).Pow(n) - ModInt.MNcr(n, a) - ModInt.MNcr(n, b) - 1;
            WriteLine(ans);
        }

        public void Display(char[] array)
        {
            var txt = "";
            foreach (var item in array)
            {
                txt += " " + item;
            }
            WriteLine("{0}", txt);
        }

        public void Display(int[] array)
        {
            var txt = "";
            foreach (var item in array)
            {
                txt += " " + item.ToString();
            }
            WriteLine("{0}", txt);
        }

        public void Display(int index,int[] array)
        {
            var txt = "";
            foreach (var item in array)
            {
                txt += " " + item.ToString();
            }
            WriteLine("{0} : {1}", index,txt);
        }

        public void Display(List<int>[] list) 
        {
            for (int i = 0; i < list.Length; i++)
            {
                Display(i, list[i].ToArray());
            }
        }
    }

    public class ConsoleInput
    {
        private readonly System.IO.TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
        {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }

        public string Read
        {
            get
            {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split(_separator);
                for (int i = 0; i < tmp.Length; i++)
                    inputStream.Enqueue(tmp[i]);
                return inputStream.Dequeue();
            }
        }

        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse(Read); } }
        public long ReadLong { get { return long.Parse(Read); } }
        public double ReadDouble { get { return double.Parse(Read); } }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }

    struct ModInt 
    {
        const int M = 1000000007;
        public long V;
        public ModInt(long v) { V = (v %= M) < 0 ? v + M : v; }

        public static implicit operator ModInt(long v) => new ModInt(v);
        public static ModInt operator +(ModInt x) => x;
        public static ModInt operator -(ModInt x) => -x.V;
        public static ModInt operator +(ModInt x,ModInt y) => x.V + y.V;
        public static ModInt operator -(ModInt x,ModInt y) => x.V - y.V;
        public static ModInt operator *(ModInt x,ModInt y) => x.V * y.V;
        public static ModInt operator /(ModInt x,ModInt y) => x.V * y.Inv();

        public ModInt Pow(int i) => MPow(V, i);
        public ModInt Inv() => MPow(V, M - 2);
        public override string ToString() => $"{V}";

        static long MPow(long b, int i)
        {
            for (var r = 1L; ; b = b * b % M)
            {
                if (i % 2 > 0) r = r * b % M;
                if ((i /= 2) < 1) return r;
            }
        }

        public static long MFactorial(int n) { for (long x = 1, i = 1; ; x = x * ++i % M) if (i >= n) return x; }
        public static long MNpr(int n, int r)
        {
            if (n < r) return 0;
            for (long x = 1, i = n - r; ; x = x * ++i % M) if (i >= n) return x;
        }
        public static ModInt MNcr(int n, int r) => n < r ? 0 : n - r < r ? MNcr(n, n - r) : (ModInt)MNpr(n, r) / MFactorial(r);

    }
}