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)


/*
	@・ω・@
*/

/*****/

# include <iostream>
# include <vector>
# include <algorithm>
# include <string>
# include <sstream>
# include <cmath>
# include <queue>
# include <stack>
# include <map>
# include <iomanip>	//cout << fixed << setprecision(桁数);
# include <stdexcept>
# include <functional>

//#define int long long

using namespace std;
using ll = long long;
using ld = long double;
using pll = pair<long long, long long>;
template<class T> using vec = vector<T>;

#define debug(x) (std::cerr << x)
#define debugln(x) (std::cerr << x << "\n")
#define debug_tab(n, x) (std::cerr << strMulti("\t",n) << (x) << "\n")
#define debug_cout(x) (std::cerr << #x << " = " <<  (x) << "\n")
#define debug_coutvec(x) std::cerr << #x << " = "; _debug_coutvec(x)
#define debug_tabcout(n, x) (std::cerr << strMulti("\t",n) << #x << " = " <<  (x) << "\n")
#define debug_headcout(h, x) (std::cerr << h << " = " <<  (x) << "\n")
#define debug_tabheadcout(n, h, x) (std::cerr << strMulti("\t",n) << h << " = " <<  (x) << "\n")

#define rep(i, n) for(int i=0, i##_len=(n); i<i##_len; ++i)
#define rep1(i, n) for(int i=1, i##_len=(n); i<=i##_len; ++i)
#define rrep(i, n) for(int i=(n)-1; i >= 0; --i)
#define rrep1(i, n) for(int i=(n); i > 0; --i)
#define step(i, a, n) for(int i=(a), i##_len=(a)+(n); i<i##_len; ++i)
#define rstep(i, a, n) for(int i=(a)+(n)-1, i##_len=(a); i>=i##_len; --i)
#define range(i, a, b) for(int i=(a), i##_len=(b); i<i##_len; ++i)
#define rrange(i, a, b) for(int i=(b)-1, i##_len=(a); i>=i##_len; --i)
#define repll(i, n) for(ll i=0, i##_len=(n); i<i##_len; ++i)
#define rep1ll(i, n) for(ll i=1, i##_len=(n); i<=i##_len; ++i)
#define rrepll(i, n) for(ll i=(n)-1; i >= 0; --i)
#define rrep1ll(i, n) for(ll i=(n); i > 0; --i)
#define stepll(i, a, n) for(ll i=(a), i##_len=(a)+(n); i<i##_len; ++i)
#define rstepll(i, a, n) for(ll i=(a)+(n)-1, i##_len=(a); i>=i##_len; --i)
#define rangell(i, a, b) for(ll i=(a), i##_len=(b); i<i##_len; ++i)
#define rrangell(i, a, b) for(ll i=(b)-1, i##_len=(a); i>=i##_len; --i)
#define all(x) (x).begin(), (x).end()
#define pair(a, b) make_pair(a, b)
std::string strMulti(std::string t, int n) { std::string out = ""; for (int i = 0; i < n; i++) { out += t; } return out; }
template<class T> void _debug_coutvec(vector<T> ar, string space = " ") { rep(i, ar.size()) { debug(ar[i] << space); } debugln(""); }
template<class T1, class T2> void _debug_coutvec(vector<pair<T1, T2>> ar, string space = " ") { rep(i, ar.size()) { debug(ar[i].first << "," << ar[i].second << space); } debugln(""); }
constexpr int INF = 2000000000;	// 2*10^9
constexpr ll INFL = 1ll << 60ll;

template<class T> bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
template<class T> T divup(T a, T b) { if (a % b == 0) { return a / b; } return a / b + 1; }
template<class T> bool cmp_2nd(pair<T, T> a, pair<T, T> b) { if (a.second != b.second) { return a.second < b.second; } return a.first < b.first; }
template<class T> T mod_pow(T x, T n, const T& p) { T ret = 1; while (n > 0) { if (n & 1) { (ret *= x) %= p; } (x *= x) %= p; n >>= 1; } return ret; }
//template<class T> T math_P(T m, T n) { T ret = 1; for (T i = m; i > m - n; i--) { ret *= i; } return ret; }
//template<class T> T math_C(T m, T n) { T ret = math_P(m, n); for (T i = 2; i <= n; i++) { ret /= i; } return ret; }
template<class T> T math_gcd(T a, T b) { if (b == 0) { return a; } else { return math_gcd(b, a % b); } }

constexpr ll MOD = 1000000007;	// 10^9+7

/*****/

// mod. m での a の逆元 a^{-1} を計算する
long long modinv(long long a, long long m) {
	long long b = m, u = 1, v = 0;
	while (b) {
		long long t = a / b;
		a -= t * b; swap(a, b);
		u -= t * v; swap(u, v);
	}
	u %= m;
	if (u < 0) u += m;
	return u;
}

template<class T> T math_P(T m, T n)
{
	T ret = 1;
	for (T i = m; i > m - n; i--)
	{
		ret = (ret * i) % MOD;
	}
	return ret;
}
template<class T> T math_C(T m, T n)
{
	T ret = math_P(m, n);
	T div = 1;
	for (T i = 2; i <= n; i++)
	{
		div = (div * i) % MOD;
	}
	ret = (ret * modinv(div, MOD)) % MOD;
	return ret;
}

void Main()
{
	ll n, a, b;
	cin >> n >> a >> b;

	ll ret = mod_pow(2ll, n, MOD) - 1;

	ret -= math_C(n, a);
	ret -= math_C(n, b);

	ret += 2 * MOD;

	cout << ret % MOD;
}

/*****/

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

	//std::cout << std::fixed << std::setprecision(10);

	/**
	while (true)
	{
		Main();
		std::cerr << flush;
		cout << endl;
	}
	/*/
	Main();
	std::cerr << flush;
	cout << endl;
	/**/

	return 0;
}