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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;

ll fact(ll n)
{
	ll ans=1;
	if(n==1 ||n==0)
	{
		return 1;
	}
	else
	{
		for(int i=1;i<=n;i++)
		{
			ans*=i;
			ans%=1000000007;
		}
		return ans;
	}
}
ll combination(ll a,ll b)
{
     double x=double(fact(a)%1000000007);
    double y=double(1)/double(fact(b));
    double z=double(1)/double(fact(a-b));
    int j=int(x*y*z);
    return (j)%1000000007;
}
typedef long long ll;
#define test() ll t;cin>>t;while(t--)
int main()
{
    ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
	ll n;
	ll a,b;
	ll ans=1;
	cin>>n>>a>>b;
	ll anss=1;
	for(int i=1;i<=n;i++)
	{
	   ans=(ans*2);
	  ans%=1000000007;
	}
	ll realans=ans-1;
	cout<<(realans-combination(n,a)-combination(n,b))%1000000007;
			
		
}