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.Linq;
using System.Collections.Generic;

namespace Contest
{
    partial class Program
    {
        static void Main(string[] args)
        {
            ABC156D();
        }

        static void ABC156A()
        {
            var nr = ReadIntN();
            var N = nr[0];
            var R = nr[1];
            Console.WriteLine(N >= 10 ? R : R + 100 * (10 - N));
        }
        static void ABC156B()
        {
            var nk = ReadIntN();
            var N = nk[0];
            var K = nk[1];
            int keta = 0;
            while (N > 0)
            {
                N /= K;
                keta++;
            }
            Console.WriteLine(keta);
        }
        static void ABC156C()
        {
            var N = ReadInt();
            var X = ReadIntN();

            int min = Int32.MaxValue;
            for(int p = 1; p <= 100; ++p)
            {
                var cost = X.Select(x => (x - p) * (x - p)).Sum();
                min = Math.Min(min, cost);
            }
            Console.WriteLine(min);
        }
        static void ABC156D()
        {
            var nab = ReadIntN();
            var N = nab[0];
            var A = nab[1];
            var B = nab[2];

            var inv = Enumerable.Range(0, 200001).Select(x => Util.Inverse(x, Util.P)).ToArray();
            Func<int, int, long> func = (X, Y) =>
            {
                long mult = 1;
                for(int i = 1; i <= Y; ++i)
                {
                    mult = (((mult * (X + 1 - i)) % Util.P) * inv[i]) % Util.P;
                }
                return mult;
            };


            long[] pow1 = new long[40];
            long[] pow2 = new long[40];
            pow1[0] = 1;
            pow2[0] = 2;
            for (int i = 1; i < pow1.Length; ++i)
            {
                pow1[i] = (pow1[i - 1] * 2);
                pow2[i] = (pow2[i - 1] * pow2[i - 1]) % Util.P;
            }
            long total = 1;

            for (int i = 0; i < pow1.Length; ++i)
            {
                if ((N & pow1[i]) > 0)
                {
                    total = (total * pow2[i]) % Util.P;
                }
            }

            total += Util.P - 1;
            total = (total + Util.P * 2 - func(N, A)) % Util.P;
            total = (total + Util.P * 2 - func(N, B)) % Util.P;
            Console.WriteLine(total);
        }
        static void ABC156E()
        {

        }
        static void ABC156F()
        {

        }


        class Util
        {
            public static readonly long P = 1000000007;

            public static long GCD(long a, long b)
            {
                while (a % b > 0)
                {
                    var c = a % b;
                    a = b;
                    b = c;
                }
                return b;
            }
            public static Dictionary<long,int> Factorize(long x)
            {
                var dict = new Dictionary<long, int>();
                long minp = 2;
                while (x > 1)
                {
                    bool ok = false;
                    for(long p = minp; p * p <= x; ++p)
                    {
                        if (x % p == 0)
                        {
                            if (!dict.ContainsKey(p))
                            {
                                dict.Add(p, 0);
                            }
                            dict[p]++;
                            minp = p;
                            x /= p;
                            ok = true;
                            break;
                        }
                    }
                    if (!ok)
                    {
                        if (!dict.ContainsKey(x)) { dict.Add(x, 0); }
                        dict[x]++;
                        break;
                    }
                }
                return dict;
            }
            public static long Inverse(long a, long p)
            {
                long b = p, c = 1, d = 0, e = 0, f = 0;
                while (b != 0)
                {
                    e = a / b;
                    f = b; b = a - e * b; a = f;
                    f = d; d = c - e * d; c = f;
                }
                c %= p;
                return c + (c < 0 ? p : 0);
            }
            public static long[] Facts(int n, long p)
            {
                var facts = new long[n + 1];
                facts[0] = 1;
                for (int i = 1; i <= n; ++i)
                {
                    facts[i] = (i * facts[i - 1]) % p;
                }
                return facts;
            }
            public static Func<int,int,long> Combin(int n, long P)
            {
                var fact = Facts(n, P);
                var inv = fact.Select(x => Inverse(x, P)).ToArray();
                return (N, M) =>
                {
                    if (N < 0 || N < M || M < 0) { return 0; }
                    return (((fact[N] * inv[M]) % P) * inv[N - M]) % P;
                };
            }
        }
        class Geometric
        {
            /// <summary>
            /// 2点間の距離
            /// </summary>
            public static double Distance(Tuple<double, double> s, Tuple<double, double> t)
            {
                var diff1 = s.Item1 - t.Item1;
                var diff2 = s.Item2 - t.Item2;
                return Math.Sqrt(diff1 * diff1 + diff2 * diff2);
            }
            /// <summary>
            /// 2点の中点
            /// </summary>
            public static Tuple<double,double> Center(Tuple<double, double> s, Tuple<double, double> t)
            {
                return new Tuple<double, double>((s.Item1 + t.Item1) / 2, (s.Item2 + t.Item2) / 2);
            }

            /// <summary>
            /// 垂直二等分線 ax+by+c=0の係数(a,b,c)を出力
            /// </summary>
            public static Tuple<double,double,double> Bisector(Tuple<double, double> s, Tuple<double, double> t)
            {
                var a = t.Item1 - s.Item1;
                var b = t.Item2 - s.Item2;
                var c = -a * (s.Item1 + t.Item1) / 2 - b * (s.Item2 + t.Item2) / 2;
                return new Tuple<double, double, double>(a, b, c);
            }

            /// <summary>
            /// 2本の直線が平行か(絶対誤差Epsilon)
            /// </summary>
            public static bool IsParallel(Tuple<double, double, double> line1, Tuple<double, double, double> line2, double epsilon)
            {
                return Math.Abs(line1.Item1 * line2.Item2 - line1.Item2 * line2.Item1) < epsilon;
            }

            /// <summary>
            /// 2本の直線の交点(平行でないことを仮定)
            /// </summary>
            public static Tuple<double,double> Intersection(Tuple<double, double, double> line1, Tuple<double, double, double> line2)
            {
                var div = line1.Item1 * line2.Item2 - line1.Item2 * line2.Item1;
                var x = (line1.Item2 * line2.Item3 - line1.Item3 * line2.Item2) / div;
                var y = (line1.Item3 * line2.Item1 - line1.Item1 * line2.Item3) / div;
                return new Tuple<double, double>(x, y);
            }
        }

        static string ReadStr()
        {
            return Console.ReadLine();
        }
        static string[] ReadStrN()
        {
            return Console.ReadLine().Split(' ');
        }
        static int ReadInt()
        {
            return Convert.ToInt32(Console.ReadLine());
        }
        static int[] ReadIntN()
        {
            return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray();
        }
        static long ReadLong()
        {
            return Convert.ToInt64(Console.ReadLine());
        }
        static long[] ReadLongN()
        {
            return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray();
        }
        static Tuple<string, string>[] ReadTupleStr(int n)
        {
            List<Tuple<string, string>> list = new List<Tuple<string, string>>();
            for (int i = 0; i < n; ++i)
            {
                var ab = ReadStrN();
                list.Add(new Tuple<string, string>(ab[0], ab[1]));
            }
            return list.ToArray();
        }
        static Tuple<long, long>[] ReadTupleLong(int n)
        {
            List<Tuple<long, long>> list = new List<Tuple<long, long>>();
            for (int i = 0; i < n; ++i)
            {
                var ab = ReadLongN();
                list.Add(new Tuple<long, long>(ab[0], ab[1]));
            }
            return list.ToArray();
        }
        static Tuple<double, double>[] ReadTupleDouble(int n)
        {
            List<Tuple<double, double>> list = new List<Tuple<double, double>>();
            for (int i = 0; i < n; ++i)
            {
                var ab = ReadLongN();
                list.Add(new Tuple<double, double>(ab[0], ab[1]));
            }
            return list.ToArray();
        }
    }
}