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 <cmath>
#include <algorithm>
#include <vector>
#include <numeric>
#include <queue>
#include <stack>
#include <map> 
#include <set>
#include <string>
#include <functional>
#include <list>
#include <random>
#include <time.h>
#include <iomanip>
#include <assert.h>
#include <numeric>
using namespace std;
using int64 = long long;
const int mod = 1e9 + 7;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
	IoSetup() {
		cin.tie(nullptr);
		ios::sync_with_stdio(false);
		cout << fixed << setprecision(10);
		cerr << fixed << setprecision(10);
	}
} iosetup;


template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {
	os << p.first << " " << p.second;
	return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
	is >> p.first >> p.second;
	return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
	for (int i = 0; i < (int)v.size(); i++) {
		os << v[i] << (i + 1 != v.size() ? " " : "");
	}
	return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
	for (T &in : v) is >> in;
	return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
	return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
	return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
	t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
	for (auto &e : t) fill_v(e, v);
}

namespace FastFourierTransform {
	using real = double;

	struct C {
		real x, y;

		C() : x(0), y(0) {}

		C(real x, real y) : x(x), y(y) {}

		inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }

		inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }

		inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }

		inline C conj() const { return C(x, -y); }
	};

	const real PI = acosl(-1);
	int base = 1;
	vector< C > rts = { { 0, 0 },
	{ 1, 0 } };
	vector< int > rev = { 0, 1 };


	void ensure_base(int nbase) {
		if (nbase <= base) return;
		rev.resize(1 << nbase);
		rts.resize(1 << nbase);
		for (int i = 0; i < (1 << nbase); i++) {
			rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
		}
		while (base < nbase) {
			real angle = PI * 2.0 / (1 << (base + 1));
			for (int i = 1 << (base - 1); i < (1 << base); i++) {
				rts[i << 1] = rts[i];
				real angle_i = angle * (2 * i + 1 - (1 << base));
				rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
			}
			++base;
		}
	}

	void fft(vector< C > &a, int n) {
		assert((n & (n - 1)) == 0);
		int zeros = __builtin_ctz(n);
		ensure_base(zeros);
		int shift = base - zeros;
		for (int i = 0; i < n; i++) {
			if (i < (rev[i] >> shift)) {
				swap(a[i], a[rev[i] >> shift]);
			}
		}
		for (int k = 1; k < n; k <<= 1) {
			for (int i = 0; i < n; i += 2 * k) {
				for (int j = 0; j < k; j++) {
					C z = a[i + j + k] * rts[j + k];
					a[i + j + k] = a[i + j] - z;
					a[i + j] = a[i + j] + z;
				}
			}
		}
	}

	vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) {
		int need = (int)a.size() + (int)b.size() - 1;
		int nbase = 1;
		while ((1 << nbase) < need) nbase++;
		ensure_base(nbase);
		int sz = 1 << nbase;
		vector< C > fa(sz);
		for (int i = 0; i < sz; i++) {
			int x = (i < (int)a.size() ? a[i] : 0);
			int y = (i < (int)b.size() ? b[i] : 0);
			fa[i] = C(x, y);
		}
		fft(fa, sz);
		C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
		for (int i = 0; i <= (sz >> 1); i++) {
			int j = (sz - i) & (sz - 1);
			C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
			fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
			fa[i] = z;
		}
		for (int i = 0; i < (sz >> 1); i++) {
			C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
			C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
			fa[i] = A0 + A1 * s;
		}
		fft(fa, sz >> 1);
		vector< int64_t > ret(need);
		for (int i = 0; i < need; i++) {
			ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
		}
		return ret;
	}


};

template< int mod >
struct ModInt {
	int x;

	ModInt() : x(0) {}

	ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

	ModInt &operator+=(const ModInt &p) {
		if ((x += p.x) >= mod) x -= mod;
		return *this;
	}

	ModInt &operator-=(const ModInt &p) {
		if ((x += mod - p.x) >= mod) x -= mod;
		return *this;
	}

	ModInt &operator*=(const ModInt &p) {
		x = (int)(1LL * x * p.x % mod);
		return *this;
	}

	ModInt &operator/=(const ModInt &p) {
		*this *= p.inverse();
		return *this;
	}

	ModInt operator-() const { return ModInt(-x); }

	ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

	ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

	ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

	ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

	bool operator==(const ModInt &p) const { return x == p.x; }

	bool operator!=(const ModInt &p) const { return x != p.x; }

	ModInt inverse() const {
		int a = x, b = mod, u = 1, v = 0, t;
		while (b > 0) {
			t = a / b;
			swap(a -= t * b, b);
			swap(u -= t * v, v);
		}
		return ModInt(u);
	}

	ModInt pow(int64_t n) const {
		ModInt ret(1), mul(x);
		while (n > 0) {
			if (n & 1) ret *= mul;
			mul *= mul;
			n >>= 1;
		}
		return ret;
	}

	friend ostream &operator<<(ostream &os, const ModInt &p) {
		return os << p.x;
	}

	friend istream &operator>>(istream &is, ModInt &a) {
		int64_t t;
		is >> t;
		a = ModInt< mod >(t);
		return (is);
	}

	static int get_mod() { return mod; }
};

using modint = ModInt< mod >;


template< typename T >
struct ArbitraryModConvolution {
	using real = FastFourierTransform::real;
	using C = FastFourierTransform::C;

	ArbitraryModConvolution() = default;

	vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {
		if (need == -1) need = a.size() + b.size() - 1;
		int nbase = 0;
		while ((1 << nbase) < need) nbase++;
		FastFourierTransform::ensure_base(nbase);
		int sz = 1 << nbase;
		vector< C > fa(sz);
		for (int i = 0; i < a.size(); i++) {
			fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);
		}
		fft(fa, sz);
		vector< C > fb(sz);
		for (int i = 0; i < b.size(); i++) {
			fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);
		}
		fft(fb, sz);
		real ratio = 0.25 / sz;
		C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
		for (int i = 0; i <= (sz >> 1); i++) {
			int j = (sz - i) & (sz - 1);
			C a1 = (fa[i] + fa[j].conj());
			C a2 = (fa[i] - fa[j].conj()) * r2;
			C b1 = (fb[i] + fb[j].conj()) * r3;
			C b2 = (fb[i] - fb[j].conj()) * r4;
			if (i != j) {
				C c1 = (fa[j] + fa[i].conj());
				C c2 = (fa[j] - fa[i].conj()) * r2;
				C d1 = (fb[j] + fb[i].conj()) * r3;
				C d2 = (fb[j] - fb[i].conj()) * r4;
				fa[i] = c1 * d1 + c2 * d2 * r5;
				fb[i] = c1 * d2 + c2 * d1;
			}
			fa[j] = a1 * b1 + a2 * b2 * r5;
			fb[j] = a1 * b2 + a2 * b1;
		}
		fft(fa, sz);
		fft(fb, sz);
		vector< T > ret(need);
		for (int i = 0; i < need; i++) {
			int64_t aa = llround(fa[i].x);
			int64_t bb = llround(fb[i].x);
			int64_t cc = llround(fa[i].y);
			aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
			ret[i] = aa + (bb << 15) + (cc << 30);
		}
		return ret;
	}
};

template< typename T >
struct Combination {
	vector< T > _fact, _rfact, _inv;

	Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
		_fact[0] = _rfact[sz] = _inv[0] = 1;
		for (int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
		_rfact[sz] /= _fact[sz];
		for (int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
		for (int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
	}

	inline T fact(int k) const { return _fact[k]; }

	inline T rfact(int k) const { return _rfact[k]; }

	inline T inv(int k) const { return _inv[k]; }

	T P(int n, int r) const {
		if (r < 0 || n < r) return 0;
		return fact(n) * rfact(n - r);
	}

	T C(int p, int q) const {
		if (q < 0 || p < q) return 0;
		return fact(p) * rfact(q) * rfact(p - q);
	}

	T H(int n, int r) const {
		if (n < 0 || r < 0) return (0);
		return r == 0 ? 1 : C(n + r - 1, r);
	}
};

template< typename T >
T factorial(int64_t n) {
	if (n >= T::get_mod()) return 0;
	if (n == 0) return 1;

	const int sn = sqrt(n);
	const T sn_inv = T(1) / sn;

	Combination< modint > comb(sn);
	using P = vector< T >;
	ArbitraryModConvolution< modint > fft;

	auto shift = [&](const P &f, T dx) {
		int n = (int)f.size();
		T a = dx * sn_inv;
		auto p1 = P(f);
		for (int i = 0; i < n; i++) {
			T d = comb.rfact(i) * comb.rfact((n - 1) - i);
			if (((n - 1 - i) & 1)) d = -d;
			p1[i] *= d;
		}
		auto p2 = P(2 * n);
		for (int i = 0; i < p2.size(); i++) {
			p2[i] = (a.x + i - n) <= 0 ? 1 : a + i - n;
		}
		for (int i = 1; i < p2.size(); i++) {
			p2[i] *= p2[i - 1];
		}
		T prod = p2[2 * n - 1];
		T prod_inv = T(1) / prod;
		for (int i = 2 * n - 1; i > 0; --i) {
			p2[i] = prod_inv * p2[i - 1];
			prod_inv *= a + i - n;
		}
		p2[0] = prod_inv;
		auto p3 = fft.multiply(p1, p2, (int)p2.size());
		p1 = P(p3.begin() + p1.size(), p3.begin() + p2.size());
		prod = 1;
		for (int i = 0; i < n; i++) {
			prod *= a + n - 1 - i;
		}
		for (int i = n - 1; i >= 0; --i) {
			p1[i] *= prod;
			prod *= p2[n + i] * (a + i - n);
		}
		return p1;
	};
	function< P(int) > rec = [&](int64_t n) {
		if (n == 1) return P({ 1, 1 + sn });
		int nh = n >> 1;
		auto a1 = rec(nh);
		auto a2 = shift(a1, nh);
		auto b1 = shift(a1, sn * nh);
		auto b2 = shift(a1, sn * nh + nh);
		for (int i = 0; i <= nh; i++) a1[i] *= a2[i];
		for (int i = 1; i <= nh; i++) a1.emplace_back(b1[i] * b2[i]);
		if (n & 1) {
			for (int64_t i = 0; i < n; i++) {
				a1[i] *= n + 1LL * sn * i;
			}
			T prod = 1;
			for (int64_t i = 1LL * n * sn; i < 1LL * n * sn + n; i++) {
				prod *= (i + 1);
			}
			a1.push_back(prod);
		}
		return a1;
	};
	auto vs = rec(sn);
	T ret = 1;
	for (int64_t i = 0; i < sn; i++) ret *= vs[i];
	for (int64_t i = 1LL * sn * sn + 1; i <= n; i++) ret *= i;
	return ret;
}

modint myBinom(int n, int r) {
	if (r == 0) {
		return modint(1);
	}
	return factorial<modint>(n) / (factorial<modint>(r) * factorial<modint>(n-r));
}

int main() {
	long long n;
	scanf("%lld", &n);
	long long a;
	scanf("%lld", &a);
	long long b;
	scanf("%lld", &b);
	//solve(n, a, b);

	modint signCk = modint(2).pow(n);

	//cout << signCk << "\n";
	//cout << myBinom(4, 2) << "\n";
	//cout << myBinom(n, 0) << "\n";
	//cout << myBinom(n, a) << "\n";

	//cout << myBinom(n, b) << "\n";


	modint ans = signCk - myBinom(n, 0) - myBinom(n, a) - myBinom(n, b);

	cout << ans << "\n";
}