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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.util.Scanner;

/**
 * @author yoshizaki
 *
 */
public class Main {
    public static void main(String[] args) {
        Scanner scanner= new Scanner(System.in);
        long kind = scanner.nextLong();
        int forbbiden1 = scanner.nextInt();
        int forbbiden2 = scanner.nextInt();
        double nfact = fact(kind);
        double rfact = 1;
        double nrfact = 1;
        double ans = 0;
        for (double r = 1; r < kind ; r++) {
            rfact = fact(r);
            nrfact = fact(kind - r);
            ans += nfact / (rfact * nrfact);
        }
        ans += 1;
        nfact = fact(forbbiden1);
        rfact = 1;
        nrfact = 1;
        for (double r = 1; r < forbbiden1 ; r++) {
            rfact = fact(r);
            nrfact = fact(forbbiden1 - r);
            ans -= nfact / (rfact * nrfact);
        }
        ans -= 1;
        nfact = fact(forbbiden2);
        rfact = 1;
        nrfact = 1;
        for (double r = 1; r <= forbbiden2 ; r++) {
            rfact = fact(r);
            nrfact = fact(forbbiden2 - r);
            ans -= nfact / (rfact * nrfact);
        }
        ans -= 1;
        System.out.println(ans % 1000000007);
    }
    static double fact(double n) {
        double nfact = 1;
        for(double i = 1; i <= n ; i++) {
            nfact *= i;
        }
        return nfact;
    }
}