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.Numerics;
using System.Linq;
using System.Text;
using static System.Math;

class MainClass
{
   static long Mod = (long)Pow(10, 9) + 7;

    public static void Main(string[] args)
    {
        var _ = LnLngs();
        var n = _[0];
        var a = _[1];
        var b = _[2];
        var max = PowLite(2, n) - 1;
        max %= Mod;

        //Remove the containts whose flower num equals a;
        var conboA = 1L;
        var reciprocalA = 1L;
        for (long i = 0; i < a; i++)
        {
            conboA = (conboA * (n - i)) % Mod;
            reciprocalA = (reciprocalA * (a - i)) % Mod;
        }
        max -= conboA * PowLite(reciprocalA, Mod - 2);
        max %= Mod;

        //Remove the containts whose flower num equals b;
        var conboB = 1L;
        var reciprocalB = 1L;
        for (long i = 0; i < b; i++)
        {
            conboB = (conboB * (n - i)) % Mod;
            reciprocalB = (reciprocalB * (b - i)) % Mod;
        }
        max -= conboB * PowLite(reciprocalB, Mod - 2);
        max %= Mod;

        while (max < 0)
        {
            max += Mod;
        }
        print(max);
    }


public static long PowLite(long n, long p, int mod = (int)1e9 + 7){long ans = 1;long now = n;for (; p > 0; p >>= 1){if ((p & 1) == 1){ans *= now;ans %= mod;}now *= now;now %= mod;}return ans;}
public static void print(object obj) { Console.WriteLine(obj); }
public static long Gcd(long a, long b) { if (a > b) { var r = a % b; if (r == 0) return b; else return Gcd(b, r); } else { var r = b % a; if (r == 0) return a; else return Gcd(a, r); } }
public static int Gcd(int a, int b) { if (a > b) { var r = a % b; if (r == 0) return b; else return Gcd(b, r); } else { var r = b % a; if (r == 0) return a; else return Gcd(a, r); } }
public static int[] LnInts() { var vs = Console.ReadLine().Trim().Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries); var ins = new int[vs.Length]; for (int i = 0; i < vs.Length; i++) ins[i] = int.Parse(vs[i]); return ins; }
public static int LnInt() { var vs = Console.ReadLine().Trim(); return int.Parse(vs); }
public static long[] LnLngs() { var vs = Console.ReadLine().Trim().Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries); var ins = new long[vs.Length]; for (int i = 0; i < vs.Length; i++) ins[i] = long.Parse(vs[i]); return ins; }
public static long LnLng() { var vs = Console.ReadLine().Trim(); return long.Parse(vs); }
public static string[] LnStrs() { var vs = Console.ReadLine().Trim().Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries); return vs; }
public static string LnStr() { var vs = Console.ReadLine().Trim(); return vs; }
public static List<T[]> AllPermutation<T>(params T[] array) where T : IComparable{var a = new List<T>(array).ToArray();var res = new List<T[]>();res.Add(new List<T>(a).ToArray());var n = a.Length;var next = true;while (next){next = false;int i;for (i = n - 2; i >= 0; i--){if (a[i].CompareTo(a[i + 1]) < 0) break;}if (i < 0) break;var j = n;do{j--;} while (a[i].CompareTo(a[j]) > 0);if (a[i].CompareTo(a[j]) < 0){var tmp = a[i];a[i] = a[j];a[j] = tmp;Array.Reverse(a, i + 1, n - i - 1);res.Add(new List<T>(a).ToArray());next = true;}}return res;}}