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: Accepted)


import java.util.Scanner;
public class Main {
	static long []fac;
	static long []finv;
	static long []inv;
	
	static int mod = 1000000007;
	static int n,a,b;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		n = Integer.parseInt(sc.next());
		
		a = Integer.parseInt(sc.next());
		b = Integer.parseInt(sc.next());
		
		fac = new long [501001];
		finv = new long[501001];
		inv = new long [501001];
		
		COMinit();
		
		
		long ans = Modpow(2L,n) -1;
		
		long aa = 1L;
		long bb = 1L;
		
		for(int i = n ; i >= n - a + 1 ; i--) {
			aa *= i;
			aa %= mod;
		}
		
		for(int i = n ; i >= n - b +1 ; i--) {
			bb *= i;
			bb %= mod;
		}
		
		aa = aa * finv[a] % mod;
		bb = bb * finv[b] % mod;
		
		ans = ans - aa - bb;
		
		ans += 2 * mod;
		
		ans = ans % mod;
		
		System.out.println(ans);

	}
	public static void COMinit() {
	    fac[0] = fac[1] = 1;
	    finv[0] = finv[1] = 1;
	    inv[1] = 1;
	    for (int i = 2; i <= 500001; 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;
	    }
	}

	// 二項係数計算
	public static long COM(int k){
	    if (n < k) return 0;
	    if (n < 0 || k < 0) return 0;
	    return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
	}

	//a^n mod
	public static long Modpow(long a, long n) {
		long res = 1;
		while(n > 0) {
			if((n & 1) == 1) {
				res = res * a % mod;
			}
			a = a * a % mod;
			n >>= 1;
		}
		return res;
	}
	



}