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)


#if TEST
using Microsoft.VisualStudio.TestTools.UnitTesting;
using Newtonsoft.Json;
#endif

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Diagnostics.Contracts;
using System.Linq;
using System.Numerics;

namespace at_coder
{
#if TEST
    [TestClass]
#endif
    public class Test_156_d
    {
        
#if TEST
        public static void Test_Main()
#else
        public static void Main()
#endif
        {
            var ar = ReadIntArray();

            int n = ar[0];
            int a = ar[1];
            int b = ar[2];

            var solve = new Solve2();

            Console.WriteLine(solve.Calc(n,a,b).ToString());
        }

        /// <summary>
        /// 10^9 + 7
        /// </summary>
        static int BIGNUM = 1000000000 + 7;

        class Solve2
        {
            public int Calc(int n, int a, int b)
            {
                BigInteger aH = new BigInteger(n);
                BigInteger aL = BigInteger.One;
                BigInteger com = BigInteger.One;

                BigInteger sum = BigInteger.Zero;
                for (int i = 1; i <= n; i++)
                {
                    com *= aH;
                    com /= aL;

                    aH = aH - 1;
                    aL = aL + 1;

                    if (i == a) continue;
                    if (i == b) continue;

                    sum += com;

                }

                BigInteger ans =  sum % (new BigInteger(BIGNUM));
                return (int)ans;
            }
        }

        class Solve1
        {
            public int Calc(int n, int a, int b)
            {

                int sum = 0;
                for (int i = 1; i <= n; i++)
                {
                    if (i == a) continue;
                    if (i == b) continue;
                    sum += com(n, i);
                }

                return sum;
            }

            int com(int n , int i)
            {
                int a = 1;
                for(int t = 0; t < i; t++)
                {
                    a *= (n - t);
                    a /= (1 + t);
                }

                return a;
            }
        }



        private static int[] ReadIntArray()
        {
            string[] ss = Console.ReadLine().Split(new char[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
            int[] ar = new int[ss.Length];
            for (int i = 0; i < ss.Length; i++)
            {
                ar[i] = int.Parse(ss[i]);
            }
            return ar;
        }
#if TEST
#else
    }
}
#endif