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.RegularExpressions;
using static kyoupuro.Input;
using static kyoupuro.MyMath;
using static kyoupuro.Modular;

namespace kyoupuro {

    class MainClass {

        private static readonly int MAX = 300000;
        static long[] fac = new long[MAX], finv = new long[MAX], inv = new long[MAX];

        // テーブルを作る前処理
        static void COMinit() {
            fac[0] = fac[1] = 1;
            finv[0] = finv[1] = 1;
            inv[1] = 1;
            for (int i = 2; i < MAX; 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
        static long COM(int n, int k) {
            if (n < k) return 0;
            if (n < 0 || k < 0) return 0;
            if (k == 0) return 1;
            if (n == 0) return 0;

            long sum = 1;
            for (int i = 0; i < k; i++) {
                sum = (sum * (n - i)) % mod;
            }

            return (sum * finv[k]) % mod;
        }

        public static void Main() {
            int N = NextInt, a = NextInt, b = NextInt;

            COMinit();

            var value = Pow(new Modular(2), N) - COM(N, a) - COM(N, b) - 1;

            Console.WriteLine(value.value);
        }
    }

    class MyMath {
        public static long Gcd(long a, long b) {
            return b == 0 ? a : Gcd(b, a % b);
        }

        public static long Sqrt(long n) {
            if (n < 0) return 0;
            long a = 0, tmp = 0, b = 0;
            for (int i = 62; i >= 0; i -= 2) {
                tmp = (b << 1) + 1 <= (n >> i) ? 1 : 0;
                a = a << 1 | tmp;
                n -= (((b << 1) + 1) * tmp) << i;
                b = (b << 1) + tmp + tmp;
            }
            return a;
        }

        public static long Nck(int n, int k) {
            if (k == 0) return 1;
            if (n == 0) return 0;
            return n * Nck(n - 1, k - 1) / k;
        }
    }

    class Modular {
        public const int mod = 1000000007;
        public readonly long value;
        public Modular(long value) { this.value = value; }
        public static implicit operator Modular(long a) {
            var m = a % mod;
            return new Modular((m < 0) ? m + mod : m);
        }
        public static Modular operator +(Modular a, Modular b) {
            return a.value + b.value;
        }
        public static Modular operator -(Modular a, Modular b) {
            return a.value - b.value;
        }
        public static Modular operator *(Modular a, Modular b) {
            return a.value * b.value;
        }
        public static Modular Pow(Modular a, int n) {
            switch (n) {
                case 0:
                    return 1;
                case 1:
                    return a;
                default:
                    var p = Pow(a, n / 2);
                    return p * p * Pow(a, n % 2);
            }
        }
        public static Modular operator /(Modular a, Modular b) {
            return a * Pow(b, mod - 2);
        }
        private static readonly List<int> facs = new List<int> { 1 };
        private static Modular Fac(int n) {
            for (int i = facs.Count; i <= n; ++i) {
                facs.Add((int)(Math.BigMul(facs.Last(), i) % mod));
            }
            return facs[n];
        }
        public static Modular Ncr(int n, int r) {
            return (n < r) ? 0
                 : (n == r) ? 1
                            : Fac(n) / (Fac(r) * Fac(n - r));
        }
        public static explicit operator int(Modular a) {
            return (int)a.value;
        }
    }

    public class PriorityQueue<T> {

        readonly List<T> _heap = new List<T>();
        readonly Comparison<T> _comparison;

        public PriorityQueue(Comparison<T> comparison) {
            _comparison = comparison;
        }

        public PriorityQueue() : this(Comparer<T>.Default.Compare) { }

        public PriorityQueue(IComparer<T> comparer) : this(comparer.Compare) { }

        public void Enqueue(T item) {
            _heap.Add(item);

            int childID = _heap.Count - 1;
            int parentID = (childID - 1) / 2;

            while (childID > 0 && _comparison(_heap[parentID], _heap[childID]) > 0) {
                Swap(parentID, childID);
                childID = parentID;
                parentID = (parentID - 1) / 2;
            }
        }

        public T Dequeue() {
            var first = _heap.First();
            _heap[0] = _heap.Last();
            _heap.RemoveAt(_heap.Count - 1);

            int parentID = 0;
            int childID = parentID * 2 + 2;
            if (childID >= _heap.Count || _comparison(_heap[childID], _heap[childID - 1]) > 0) childID--;

            while (childID < _heap.Count && _comparison(_heap[parentID], _heap[childID]) > 0) {
                Swap(parentID, childID);
                parentID = childID;
                childID = parentID * 2 + 2;
                if (childID >= _heap.Count || _comparison(_heap[childID], _heap[childID - 1]) > 0) childID--;
            }

            return first;
        }

        void Swap(int parent, int child) {
            var tmp = _heap[parent];
            _heap[parent] = _heap[child];
            _heap[child] = tmp;
        }

        public T Peek() { return _heap[0]; }
        public int Count => _heap.Count;
        public bool Any() { return _heap.Any(); }
        public List<T> Data => _heap;
    }

    public class UnionFind {
        public int[] Parents { get; set; }
        public UnionFind(int size) {
            Parents = Enumerable.Repeat(-1, size).ToArray();
        }

        public int Find(int num) {
            if (Parents[num] < 0) return num;

            Parents[num] = Find(Parents[num]);
            return Parents[num];
        }

        public int Size(int num) {
            return -Parents[Find(num)];
        }

        public bool Same(int a, int b) {
            return Find(a) == Find(b);
        }

        public void Unite(int a, int b) {
            int x = Find(a), y = Find(b);

            if (Size(x) > Size(y)) {
                Parents[x] += Parents[y];
                Parents[y] = x;
            } else {
                Parents[y] += Parents[x];
                Parents[x] = y;
            }
        }
    }

    class Input {
        static IEnumerator<string> enumerator = new string[] { }.AsEnumerable().GetEnumerator();

        public static string Line => Console.ReadLine();

        public static string[] StrArr => Line.Split(' ');

        public static int NextInt => int.Parse(NextWord());

        public static long NextLong => long.Parse(NextWord());

        public static List<int> IntList => StrArr.Select(int.Parse).ToList();

        public static List<long> LongList => StrArr.Select(long.Parse).ToList();

        public static string NextWord() {
            while (!enumerator.MoveNext()) {
                enumerator = StrArr.AsEnumerable().GetEnumerator();
            }
            return enumerator.Current;
        }
    }
}