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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.*;
public class Main {
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    long n = sc.nextLong();
    long a = sc.nextLong();
    long b = sc.nextLong();
    long ans = modPow(2, n) - 1;
    ans = minus(ans,cmb(n,a));
    ans = minus(ans,cmb(n,b));

    System.out.println(ans);
  }
  private static final long MOD = 1000000007;
  private static final long MOD5 = 1000000005;

  private static long modPow(long a, long n) {
    if (n == 1) return a % MOD;
    if (n % 2 == 1) return (a * modPow(a, n - 1)) % MOD;
    long t = modPow(a, n / 2);
    return (t * t) % MOD;
  }

	private static long minus(long a, long b) {
      while (a<b) {
        a+=MOD;
      }
      return (a-b) % MOD;
    }
    private static long cmb(long n, long r) {
        if (n-r<r) {
            r = n - r;
        }
        long x = 1;
        long y = 1;
        for (long i=0;i<r;i++) {
            x = x * (n - i) % MOD;
            y = y * (i + 1) % MOD;            
        }
        return x * modPow(y, MOD5);
    }

}