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: Accepted)



#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define f(i, n) for(ll i=0;i<n;i++)
#define r(i, n) for(ll i=n-1;i>=0;i--)
#define forr(i, x, y) for(ll i=x;i<y;i++)
ll fastpower(ll a,ll n){
    ll res=1;
    while(n>0){
        if(n&1){
            res=(res*a)%1000000007;
        }
        a=(a*a)%1000000007;
        n>>=1;
    }
    return (res);
}
ll binomial(ll n,ll k){
    ll res=1;
    
    f(i,k){
        res=(res*(n-i))%1000000007;
        
    }
    f(i,k){
        res=(res*fastpower(i+1,1000000005))%1000000007;
    }
    return res;
}
int main()
{
    ll n,a,b;
    cin>>n>>a>>b;
    ll ans=(fastpower(2,n)-binomial(n,a)-binomial(n,b)-1+1000000007+1000000007)%1000000007;
   
    cout<<ans;

}