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)

#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 Solve4();

            Console.WriteLine(solve.Calc(n,a,b).ToString());
        }
      
      	class Solve4
        {
            public long Calc(int n, int a, int b)
            {
                ModInt all = ModInt.Pow(2, n) - 1;

                var ans = all - C(n, a) - C(n, b);

                return ans.Val;
            }

            private long C(int n, int r)
            {
                ModInt a = 1;

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

                return a.Val;
            }
        }

		class Solve3
        {
            public long Calc(int n, int a, int b)
            {
                ModInt aH = n;
                ModInt aL = 1;
                ModInt com = 1;

                ModInt sum = 0;
                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;

                }

                return sum.Val;
            }
        }
      
        struct ModInt
        {
            /// <summary>
            /// 基準となる素数
            /// </summary>
            const long MOD = 1000000007;

            public long Val { get; private set; }

            public static implicit operator ModInt(long i) { return new ModInt(i); }

            public ModInt(long n)
            {
                Val = n % MOD;
                if (Val < 0) Val += MOD;
            }

            public static ModInt ValueOf(long n)
            {
                return new ModInt(n);
            }

            public static ModInt operator +(ModInt a, ModInt b)
            {
                if (a.Val == 0) return b;
                if (b.Val == 0) return a;

                return new ModInt(a.Val + b.Val);
            }
            public static ModInt operator -(ModInt a)
            {
                if (a.Val == 0) return a;
                return ModInt.ValueOf(MOD - a.Val);

            }
            public static ModInt operator -(ModInt a, ModInt b)
            {
                return new ModInt(a.Val - b.Val);
            }
            public static ModInt operator *(ModInt a, ModInt b)
            {
                return new ModInt(a.Val * b.Val);
            }
            public static ModInt operator /(ModInt a, ModInt b)
            {
                long c = a.Val * modinv(b.Val);
                return new ModInt(c);
            }

            public static ModInt Pow(ModInt a, ModInt b)
            {
                long c = modpow(a.Val, b.Val);
                return new ModInt(c);
            }

            // https://qiita.com/drken/items/3b4fdf0a78e7a138cd9a 参照

            // a^b
            private static long modpow(long a, long n)
            {
                long res = 1;
                while (n > 0)
                {
                    if ((n & 1) != 0) res = res * a % MOD;
                    a = a * a % MOD;
                    n >>= 1;
                }
                return res;
            }

            // a^-1
            private static long modinv(long a)
            {
                long b = MOD, u = 1, v = 0;
                while (b != 0)
                {
                    long t = a / b;
                    a -= t * b; swap(ref a, ref b);
                    u -= t * v; swap(ref u, ref v);
                }
                u %= MOD;
                if (u < 0) u += MOD;
                return u;
            }

            private static void swap(ref long a, ref long b)
            {
                long t = a; a = b; b = t;
            }
            
            public static bool operator ==(ModInt a, ModInt b)
            {
                return a.Val == b.Val;
            }
            public static bool operator !=(ModInt a, ModInt b)
            {
                return a.Val != b.Val;
            }

            public override string ToString()
            {
                return this.Val.ToString();
            }

            public override int GetHashCode()
            {
                return (int) (this.Val % MOD);
            }

            public override bool Equals(object obj)
            {
                if (obj is ModInt)
                {
                    return ((ModInt)obj).Val == this.Val;
                }
                else
                {
                    return false;
                }
            }
        }
      
        /// <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