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<iostream>
#include<cstring>
#include<cstdio>
#include<cstdlib>
#include<map>
#include<ctime>
#include<algorithm>
#include<cmath>
#include<queue>
#include<set>
#include<stack>
#include<vector>
#include<bitset>
#define ll long long 
#define ull unsigned long long 
#define mem(a) memset(a,0,sizeof(a)) 
#define fio ios::sync_with_stdio(false),cin.tie(0),cout.tie(0)
#define EXIT exit(0)
#define all(a) (a).begin(),(a).end()
//loop 
#define For(i,a,b) for(int i=(a);i<(b);i++)
#define FOR(i,a,b) for(int i=(a);i<=(b);i++)
#define cFor(i,a,b) for(int i=(a);i>(b);i--)
#define cFOR(i,a,b) for(int i=(a);i>=(b);i--)
#define lFor(i,a,b) for(ll i=(a);i<(b);i++)
#define lFOR(i,a,b) for(ll i=(a);i<=(b);i++)
#define lcFor(i,a,b) for(ll i=(a);i>(b);i--)
#define lcFOR(i,a,b) for(ll i=(a);i>=(b);i--)
//debug
#define dbg(a) cout<<#a<<"="<<a<<endl
#define inthis cout<<"--------this\n"
//operator
#define pb push_back
#define ins insert
#define era erase
#define fin find 
//pair
#define pr pair
#define mkp(a,b) make_pair(a,b)
#define fi first
#define se second
//vector
#define vec vector
#define vi vector<int>
#define vii vector<vector<int>>
//map
#define mp map
////map int
#define mpii map<int,int>
#define mpib map<int,bool>
#define mpic map<int,char>
#define mpis map<int,string>
#define mpil map<int,long long>
////map long long 
#define mpll map<long long,long long>
#define mplb map<long long,bool>
#define mplc map<long long,bool>
#define mpls map<long long,string>
#define mpli map<long long,int>
////map char
#define mpci map<char,int>
#define mpcb map<char,bool>
#define mpcl map<char,long long>
////map string
#define mpsi map<string,int>
#define mpsb map<string,bool>
#define mpsl map<string,long long>
//iterator
#define ivec(a) vector<a>::iterator
#define iset(a) set<a>::iterator 
#define imp(a,b) map<a,b>::iterator

using namespace std;
/*
const int maxsize=
struct edge{
	int nod,nxt;
			
}e[maxsize<<1];
int nume=0,pa[maxsize],head[maxsize];
void add(int u,int v){
	e[++nume].nod=v;
	e[nume].nxt=head[u];
	head[u]=nume;
}
void init(){
	
}
bool vis[maxsize];
void bfs(){
	
}
void dfs(){

}
*/
const int inf=7+1e9,maxn=5+1e6;
ll dp[maxn];
ll qpow(ll a,ll p,ll mod){
	ull res=1;a%=mod;
	while(p){
		if(p&1)
			res=res*a%mod;
		a=a*a%mod;
		p>>=1;	
	}
	return res;
}
ll A=1,B=1,N=1,NA=1,NB=1;
int main(){
	fio;
	int n,a,b;
	cin>>n>>a>>b;
	ll ans=qpow(2,n,inf);
	FOR(i,2,a)
		A=A*i%inf;
	FOR(i,2,b)
		B=B*i%inf;	
	FOR(i,1,a)
		NA=NA*(n-i+1)%inf;	
	FOR(i,1,b)
		NB=NB*(n-i+1)%inf;	
	ans-=NA*qpow(A%inf,inf-2,inf)%inf;
	ans-=NB*qpow(B%inf,inf-2,inf)%inf;
	ans=(ans+inf*2)%inf;
	cout<<ans-1<<endl;
}