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: Runtime Error)

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


class Program
{
    static void Main(string[] args)
    {
        const long mod = 1000000007;

        // 入力
        long[] nab = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long n = nab[0];
        long a = nab[1];
        long b = nab[2];


        long[] sum = new long[n];
        long ans = 0;
        for (int i = 0; i < n; i++)
        {
            if (i == 0)
            {
                sum[i] = n % mod;
                
            }
            else
            {
                sum[i] = (sum[i - 1] * (n - i) / (i + 1)) % mod;
            }

            if (i == a-1 || i == b-1)
            {
                continue;
            }
            ans += sum[i];
            ans %= mod;
        }
        Console.WriteLine(ans);
    }
}