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 int
#define MOD 1000000007

ll p(ll a,ll n ,ll mod ){
    
 
    if (n == 0) {
        return 1;
    }
    ll res = p(a * a % mod, n / 2, mod);
    if (n & 1) {
        res = res*a %mod;
    }
    return res;

}

ll modInv(ll n,ll m){
  return p(n,m-2 , m);
}

ll nCr(ll n, ll r ){
    long long a=1;
    long long b=1;
    long long inv=0;
 
    for(ll i=0; i< r; i++){
        a = (a*(n-i)) % MOD;
    }
    for(ll i=1; i<= r; i++){
        b = (b*i) % MOD;
    }
    inv = p(b, MOD-2 ,MOD);
 
    return (a*inv) %MOD;

}

int main(){ 
    long long int n,a,b;
    cin>>n;
    cin>>a;
    cin>>b;
    
    ll ans = p(2,n,MOD)-1 - nCr(n,a) - nCr(n,b);

   ans = (ans%MOD + MOD) % MOD;

        cout<<ans<<endl;
      

    
    return 0;
}