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>
#define REP(i,n) for(int i=0,i##_len=int(n);i<i##_len;++i)
#define rep(i,a,b) for(int i=int(a);i<int(b);++i)
#define All(x) (x).begin(),(x).end()
#define rAll(x) (x).rbegin(),(x).rend()
using namespace std;
using ll = long long;

constexpr ll mod = 1e9+7;
ll mpow(ll a,ll n){
    ll ans=1,x=a;
    while(n){
        if(n&1) ans=ans*x%mod;
        x=x*x%mod;
        n>>=1;
    }
    return ans;
}

ll nCr(ll n,ll r){
    ll res=1;
    for(int i=1;i<=r;++i){
        res=res*i%mod;
    }
    res=mpow(res,mod-2);
    for(int i=n;i>n-r;--i){
        res=res*i%mod;
    }
    return res;
}

int main(){
    ll n,a,b;
    cin>>n>>a>>b;
    
    ll ans=mpow(2,n);
    ans--;
    cout<<(ans-nCr(n,a)-nCr(n,b)+2*mod)%mod<<endl;
}