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;

class Program
{
    static void Main(string[] args)
    {
        int maxVal = (int)(Math.Pow(10,9) + 7);
        int[] arr = Console.ReadLine().Split(' ').Select(v => int.Parse(v)).ToArray();
        int n = arr[0];
        int a = arr[1];
        int b = arr[2];
        var ans = ModInt.Pow(2, n) - 1 - nCr(n, a) - nCr(n, b);
        Console.WriteLine(ans);

    }

    static ModInt nCr(int n, int r)
    {
        ModInt ans = 1;
        // 分子
        for (int i = 0; i < r; i++)
        {
            ans *= n - i;
        }
        // 分母
        for (int i = 1; i <= r; i++)
        {
            ans /= i;
        }
        return ans;
    }

    public struct ModInt
    {
        public const long Mod = (int)1e9 + 7;
        public long num;
        public ModInt(long n) { num = n; }
        public override string ToString() { return num.ToString(); }
        public static ModInt operator +(ModInt l, ModInt r) { l.num += r.num; if (l.num >= Mod) l.num -= Mod; return l; }
        public static ModInt operator -(ModInt l, ModInt r) { l.num -= r.num; if (l.num < 0) l.num += Mod; return l; }
        public static ModInt operator *(ModInt l, ModInt r) { return new ModInt(l.num * r.num % Mod); }
        public static ModInt operator /(ModInt l, ModInt r) { return l * Inverse(r); }
        public static implicit operator ModInt(long n) { n %= Mod; if (n < 0) n += Mod; return new ModInt(n); }
        public static ModInt Pow(ModInt v, long k) { return Pow(v.num, k); }
        public static ModInt Pow(long v, long k)
        {
            long ret = 1;
            for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
                if ((k & 1) == 1) ret = ret * v % Mod;
            return new ModInt(ret);
        }
        public static ModInt Inverse(ModInt v) { return Pow(v, Mod - 2); }
        private static List<ModInt> Facs = new List<ModInt> { 1 };
        public static ModInt Fac(int n)
        {
            for (int i = Facs.Count; i <= n; i++)
            {
                Facs.Add(i * Facs[i - 1]);
            }
            return Facs[n];
        }
        public static ModInt nCr(int n, int r)
        {
            if (n < r) return 0;
            if (n == r) return 1;
            return Fac(n) / (Fac(r) * Fac(n - r));
        }
    }



}