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)

#if defined(__GNUC__)
#include <bits/stdc++.h>
#define __int32 __int32_t
// __GNUC__
#else
#include "bits/stdc++.h"
#endif
using namespace std;

#define int long long

#define itn __int32
#define REP(i, n) for(itn (i) = 0; (i) < (n); ++(i))
#define REP2(i, x, n) for(itn (i) = x; (i) < (n); ++(i))
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define SORT(x) sort(ALL(x))
#define RSORT(x) sort(ALL(x), greater<decltype(x)::value_type>())
#define RSORT2(x, T) sort(ALL(x), greater<T>())
#define REVERSE(x) reverce(ALL(x))
#define ACM(x, y) accumulate(ALL(x), y)

#define INT_POW(x, y) [](int a, int b) -> int {int c = a; REP(i, b - 1){c *= a;} return c;}(x, y)
#define INT_POWM(x, y, m) [](int a, int b, int m) -> int {int c = a; REP(i, b - 1){c *= a; c %= m;} return c;}(x, y, m)
#define FCT(x) [](int a) -> int {int r = 1; REP(i, a){r *= i;} return r;}(x)

// デバッグ用
#define PUT_LIST(x, y) std::copy(ALL(x), ostream_iterator<decltype(x)::value_type>(cout, y))

const int kMod = 1e9 + 7;

int curPowMod(int a, int n, int m) {
	if (n == 0) {
		return 1;
	}
	else if (n == 1) {
		return a;
	}
	else if (n == 2) {
		return a * a;
	}
	else {
		int w = curPowMod(a, n / 2, m);
		w = (w * w) % m;
		return (w * ((n % 2) ? a : 1)) % m;
	}
}

itn main() {
	std::ios::sync_with_stdio(false);

	int n, a, b;

	cin >> n >> a >> b;

	if (n == 2) {
		cout << 0;
		return 0;
	}

	int all_mod_pow = curPowMod(2, n, kMod) - 1;

	int sub_ptr, a_ptr, b_ptr;
	sub_ptr = 0;

	int a_tp, a_bt;
	a_tp = n;
	a_bt = a;

	REP2(i, 1, a) {
		a_tp *= n - i;
		a_bt *= a - i;
		a_tp %= kMod;
		a_bt %= kMod;
	}

	int b_tp, b_bt;
	b_tp = n;
	b_bt = b;

	REP2(i, 1, b) {
		b_tp *= n - i;
		b_bt *= b - i;
		b_tp %= kMod;
		b_bt %= kMod;
	}

	a_ptr = (a_tp * curPowMod(a_bt, kMod - 2, kMod)) % kMod;
	b_ptr = (b_tp * curPowMod(b_bt, kMod - 2, kMod)) % kMod;

	sub_ptr = (a_ptr + b_ptr) % kMod;

	cout << all_mod_pow - sub_ptr;

	return 0;
}