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<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef unsigned long long ul;
typedef unsigned int ui;
typedef pair<int, int>P;
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
typedef vector<vector<ll>> mat;
typedef vector<ll> vec;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
const ll mod = 1000000007;
const ll INF = mod * mod;
const ld eps = 1e-12;
const ld pi = acos(-1.0);
//int qp(int a,ll b){int ans=1;do{if(b&1)ans=1ll*ans*a%mo;a=1ll*a*a%mo;}while(b>>=1);return ans;}
ll qp(ll a,ll b,int mo){int ans=1;do{if(b&1)ans=1ll*ans*a%mo;a=1ll*a*a%mo;}while(b>>=1);return ans;}
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;} // 最大公約数
ll lcm (ll a, ll b){return a/gcd(a,b)*b;} // 最小公倍数
int dx[4] = { 0,1,0,-1 };
int dy[4] = { 1,0,-1,0 };

template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template<typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template<typename T> bool chmin(T &m, const T q) { if (q < m) {m = q; return true;} else return false; }
template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }

struct mint {
    ll n;
    mint(ll a = 0) {n = a % mod;}
    mint& operator+=(mint a) {n += a.n; n %= mod; return *this;}
    mint& operator-=(mint a) {n += mod; n -= a.n; n %= mod; return *this;}
    mint& operator*=(mint a) {n *= a.n; n %= mod; return *this;}
    mint& operator%=(mint a) {n %= a.n; return *this;}
    mint& operator++() {n++;n %= mod; return *this;}
    mint& operator--() {n += mod; n--; n %= mod; return *this;}
};
mint operator+(mint a, mint b) {a += b; return a;}
mint operator-(mint a, mint b) {a -= b; return a;}
mint operator*(mint a, mint b) {a *= b; return a;}

mint factMod(ll n) {
    if (n == 0)
    {
        return 1;
    }
    mint ans = 1;
    while (n > 1) {
        ans *= n;
        n--;
    }
    return ans;
}

mint powMod(mint x, ll y) {
    if (x.n <= 1)
    {
        return x;
    }
    if (y == 0)
    {
        return 1;
    }
    else if (y == 1)
    {
        return x;
    }
    else if (y % 2 == 0)
    {
        mint tmp = powMod(x, y / 2);
        return tmp * tmp;
    }
    else
    {
        mint tmp = powMod(x, y / 2);
        return tmp * tmp * x;
    }
}

mint modinv(mint n)
{
    return powMod(n, mod - 2);
}

vector<ll> invtbl;
void preCalcInv(ll up)
{
    invtbl.resize(up + 1);
    invtbl[1] = 1;
    for(ll a=2; a<=up; a++)
    {
        invtbl[a] = mod - invtbl[mod % a] * (mod / a) % mod;
    }
}

mint operator/(mint a, mint b)
{
    if (b.n < invtbl.size())
    {
        a *= invtbl[b.n];
    }
    else
    {
        a *= modinv(b);
    }
    return a;
}
mint& operator/=(mint& a, mint b)
{
    a = a / b;
    return a;
}


mint nCrMod(ll n, ll r)
{
    if (n < r || n < 0 || r < 0)
    {
        return 0;
    }
    r = min(r, n - r);
    mint a = 1;
    for(ll i= n-r+1; i<=n; i++)
    {
        a *= i;
    }

    a /= factMod(r);
    return a;
}

mint nHrMod(ll n, ll r)
{
    return nCrMod(n + r - 1, r);
}

template<class T>
constexpr auto modK_belowN(T k, T MOD, T n)
{
    return (n + MOD - k - 1) / MOD;
}



void solve() {
    ll N,A,B;
    cin >> N >> A >> B;

    mint co = powMod((mint)2,N) - 1 - nCrMod(N,A) - nCrMod(N,B);

    cout << co.n << endl;
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    std::cout << fixed << setprecision(10);
    solve();
    // stop
        return 0;
}