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)

using System;
using System.Linq;
namespace ABC156
{
    class D
    {
        static void Main(string[] args)
        {
            long[] input = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long n = input[0];
            long a = input[1];
            long b = input[2];
            long mod = 1000000007;

            long total = modPow(2, n, mod) - 1;
            long ca = modCombination(n, a, mod) % mod;
            long cb = modCombination(n, b, mod) % mod;
            Console.WriteLine((total + mod - (ca + cb) % mod) % mod);
        }

        public static long modPow(long a, long n, long mod)
        {
            long res = 1;
            while (n > 0)
            {
                if ((n & 1) > 0) res = res * a % mod;
                a = a * a % mod;
                n >>= 1;
            }
            return res % mod;
        }
        public static long modInv(long a, long mod)
        {
            return modPow(a, mod - 2, mod) % mod;
        }

        public static long modMul(long a, long b, long mod)
        {
            return ((a % mod) * (b % mod)) % mod;
        }

        public static long modDiv(long a, long b, long mod)
        {
            return modMul(a, modInv(b, mod), mod);
        }

        private static long modCombination(long n, long k, long mod)
        {
            long answer = 1;
            for (long i = n; i > n - k; i--)
            {
                answer = modMul(answer, i, mod);
            }
            for (long i = 1; i <= k; i++)
            {
                answer = modDiv(answer, i, mod);
            }
            return answer;
        }

    }
}