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++ (GCC 5.4.1) (judge verdict: Runtime Error)

#include <iostream>
#include <cmath>
using namespace std;

int comb(int a, int b);

int comb(int a, int b) {
    int n = b, x = 1, y = 1;
    for (int i = 0; i < n; i++) {
        x *= a--;
        y *= b--;
    }
    return x / y;
}

int main(void) {
    int mod = 1e9 + 7;
    int n, a, b;
    cin >> n >> a >> b;
    int ans = 0;
    for (int i = 1; i < n+1; i++) {
        if (i == a || i == b) {
            continue;
        }
        ans += comb(n, i);
        if (ans >= mod) {
            ans = ans % mod;
        }
    }
    cout << ans << endl;
    return 0;
}