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.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		long N = long.Parse(str[0]);
		long A = long.Parse(str[1]);
		long B = long.Parse(str[2]);
		long mod = 1000000007;
		long ans = Mpow(2,N,mod);
		ans = ans + mod - Ncr(N,A,mod) + mod - Ncr(N,B,mod) - 1 + mod;
		ans %= mod;
		Console.WriteLine(ans);
	}
	
	public static long Mpow(long x,long n,long m)
	{
		long ans = 1;
		while(n > 0){
			if(n % 2 == 1){
				ans = ans * x % m;
				n -= 1;
			}
			x = x * x % m;
			n /= 2;
		}
		return ans;
	}
	public static long Ncr(long n,long r,long m)
	{
		long ans = 1;
		for(var i=n-r+1;i<=n;i++){
			ans = ans * i % m;
		}
		for(var i=2;i<=r;i++){
			ans = ans * Mpow(i,m-2,m) % m;
		}
		return ans;
	}
}