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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

class D {
    static long mod = 1000000007;
    static void Main(string[] args) {
        var st = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long n = st[0];
        long a = st[1];
        long b = st[2];


        long sum = myPow(2, n) % mod - 1;
        if (sum < 0) {
            sum += mod;
        }

        long xa = superCombinations(n, a);
        long xb = superCombinations(n, b);

        sum -= xa;
        sum -= xb;

        sum %= mod;
        if (sum < 0) {
            sum += mod;
        }

        Console.WriteLine(sum);
    }

    static long myPow(long x, long n) {
        if (n == 0)
            return 1;
        if (n % 2 == 0)
            return myPow(x * x % mod, n / 2);
        else
            return x * myPow(x, n - 1) % mod;
    }
    

    public static long superCombinations(long n, long k) {
        long count = n;

        for (long x = 1; x <= k - 1; x++) {
            count = count * (n - x) % mod * ModInv(x) % mod;
        }

        return (count * ModInv(k)) % mod;
    }

    static long FactorialMod(long a) {

        if (a <= 1) {
            return 1;
        } else {
            return a * FactorialMod(a - 1) % mod;
        }
    }

    public static long ModInv(long a) {
        if (a <= 1) {
            return 1;
        } else {
            long ret = (long)(0 - (ModInv(mod % a) * (mod / a)) % mod);
            if (ret < 0) {
                ret += (long)mod;
            }

            return (long)ret;
        }
    }

    static long FactorialModInv(long a) {
        if (a <= 1) {
            return 1;
        } else {
            return ModInv(a) * FactorialModInv(a - 1) % mod;
        }
    }
}