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: Runtime Error)

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

const int K = 10*10*10*10*10*10*10*10*10 + 7;
void comb(vector<vector <long long int> >& v) {
	for (int i = 0; i < v.size(); i++) {
		v[i][0] = 1;
		v[i][i] = 1;
	}
	for (int k = 1; k < v.size(); k++) {
		for (int j = 1; j < k; j++) {
			v[k][j] = ((v[k - 1][j - 1] + v[k - 1][j])) % K;

		}
	}
}

int main() {
	int n, a, b;
	long long int ans = 1;
	
	cin >> n >> a >> b;

	for (int i = 0; i < n; i++) {
		ans *= 2;
		ans %= K;
	}

	vector<vector<long long int> > v(n + 1, vector<long long int>(n + 1, 0));
	comb(v);
	ans -= v[n][a];
	vector<vector<long long int> > w(n + 1, vector<long long int>(n + 1, 0));
	comb(w);
	ans -= w[n][b];

	ans -= 1;
	ans %= K;

	cout << ans << endl;

	return 0;
}