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: Wrong Answer)

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];

            #region old

            //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 (i%1000==0)
            //    {
            //    Debug.WriteLine(i);

            //    }
            //}

            //return count % mod;

            #endregion

            var tolal = Modular.Pow(N, 2) - 1;
            return tolal - Modular.Combination(N, A) - Modular.Combination(N, B);
        }

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

            return _up / _down;
        }

        public class Modular
        {
            public long Value { get; private set; }

            private static readonly long _mod = (long)Math.Pow(10, 9) + 7;
            private static readonly List<int> _facCache = new List<int> { 1 };

            public static explicit operator long(Modular m) => m.Value;
            public static implicit operator Modular(long a)
            {
                var m = a % _mod;

                return new Modular
                {
                    Value = (m < 0) ? m + _mod : m
                };
            }

            public static Modular operator +(Modular a, Modular b) => a.Value + b.Value;
            public static Modular operator -(Modular a, Modular b) => a.Value - b.Value;
            public static Modular operator *(Modular a, Modular b) => a.Value * b.Value;
            public static Modular operator /(Modular a, Modular b) => a * Pow(b, _mod - 2);
            public static Modular Pow(Modular a, long 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 Factorial(long n)
            {
                for (int i = _facCache.Count; i <= n; ++i)
                {
                    var fac = (int)(Math.BigMul(_facCache.Last(), i) % _mod);
                    _facCache.Add(fac);
                }
                return _facCache[(int)n];
            }
            public static Modular Combination(long n, long r)
            {
                return (n < r) ? 0
                     : (n == r) ? 1
                     : Factorial(n) / (Factorial(r) * Factorial(n - r));
            }
            public override string ToString()
            {
                return Value.ToString();
            }
        }
    }
}