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: Runtime Error)

import java.io.*;

public class Main {
  public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    
    String[] data = br.readLine().split(" ");
    int n = Integer.parseInt(data[0]);
    int a = Integer.parseInt(data[1]);
    int b = Integer.parseInt(data[2]);
    
    COMinit();
    int result = 0;
    for(int i=1; i<=n; i++){
      if(i==a || i==b){
        continue;
      }
      result += combination(n, i);
    }
    System.out.println(result);
  }
  
  public static int MOD = 1_000_000_007;
  public static int MAX = 1_000_000_000;
  public static int[] fac = new int[MAX];
  public static int[] finv = new int[MAX];
  public static int[] inv = new int[MAX];
  
  public static void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for(int i = 2; i < MAX; i++) {
      fac[i] = fac[i-1] * i % MOD;
      inv[i] = MOD - inv[MOD%i] * (MOD/i) % MOD;
      finv[i] = finv[i-1] * inv[i] % MOD;
    }
  }
  
  public static long combination(int n, int k){
    if(n < k || n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n-k] % MOD) % MOD;
  }
}