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;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace D
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var nab = Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray();
            var p = (long)Math.Pow(10, 9) + 7;
            var all = Power(2, nab[0], p);
            var combA = CombinationCount(nab[0], nab[1], p);
            var combB = CombinationCount(nab[0], nab[2], p);
            var result = (all - combA - combB + p) % p - 1;
            Console.WriteLine(result);
        }

        static long PermutationCount(long n, long k, long mod)
        {
            if (n < k) throw new ArgumentException();
            var result = 1L;
            for (var i = 0; i < k; i++)
                result = (result * (n - i) % mod) % mod;
            return result;
        }

        static long CombinationCount(long n, long k, long mod)
        {
            if (n < k) throw new ArgumentException();
            k = Math.Min(k, n - k);
            var top = PermutationCount(n, k, mod);
            var bottom = PermutationCount(k, k, mod);
            return (top * Power(bottom, mod - 2, mod)) % mod;
        }

        static long Power(long x, long y, long mod)
        {
            var result = 1L;
            while (y > 0)
            {
                if ((y & 1) == 1) result = ((result % mod) * (x % mod)) % mod;
                x = ((x % mod) * (x % mod)) % mod;
                y >>= 1;
            }
            return result;
        }
    }
}