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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
#define mfill(x,y) memset(x,y,sizeof(x))
#define all(v) v.begin(), v.end()
#define in(x,y,h,w) if(0<=x&&x<h&&0<=y&&y<w)
#define y0 y12345
#define y1 y54321

#ifdef LOCAL
#define debug(...) fprintf(stderr,__VA_ARGS__)
#else
#define debug(...) 42
#endif

using ul = unsigned long;
using ll = long long;
using P = pair<int, int>;
using vint = vector<int>;using vvint = vector<vector<int>>;
using vll = vector<ll>;using vvll = vector<vector<ll>>;
template<class T>bool chmax(T &a, const T &b){if(a<b){a=b;return 1;}return 0;}
template<class T>bool chmin(T &a, const T &b){if(a>b){a=b;return 1;}return 0;}
template <class T>void initvv(vector<vector<T> > &v, int a, int b, const T &t = T()){
    v.assign(a, vector<T>(b, t));
}
template <class T>T gcd(T &a, T &b){if(a<b){swap(a,b);} T r = a%b; while(r!=0){a=b;b=r;r=a%b;} return b;}

vint dx = {-1, 0, 1, 0}, dy = {0, -1, 0, 1};
vint dx8 = {-1, -1, -1, 0, 1, 1, 1, 0}, dy8 = {-1, 0, 1, 1, 1, 0, -1, -1};
ll mod = 1000000007;
ll pow2(ll x, ll p){
    if(p == 0){return 1;}
    ll ret = pow2(x, p/2);
    return ((ret*ret%mod)*(p%2==1?x:1))%mod;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    debug("debug test\n");
    ll n, a, b;cin>>n>>a>>b;
    ll base = pow2(2, n) - 1;
    
    ll par = 1;
    ll chil = 1;
    for(int i = n;i>n-min(a, n-a);i--){
        //if(i<=n+1-i)break;
        par = par*i%mod;
        chil = chil*(n+1-i)%mod;
    }
    ll minusa = par*pow2(chil, mod-2) % mod;
    par = 1;
    chil = 1;
    for(int i = n;i>n-min(b, n-b);i--){
        //if(i<=n+1-i)break;
        par = par*i%mod;
        chil = chil*(n+1-i)%mod;
    }
    ll minusb = par*pow2(chil, mod-2) % mod;
    debug("nf %d\n", base);
    cout << (base - minusa - minusb + mod) % mod << endl;
    return 0;
}