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.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static void Main(){
		Sc sc=new Sc();
		var s=sc.Ia;
		Cb r=new Cb(1);
		Mint ans=Fp(2,s[0])-1;
		ans-=r.C2(s[0],s[1]);
		ans-=r.C2(s[0],s[2]);
		Console.WriteLine("{0}",ans);
	}
	static long Fp(long x,long e){
		long r=1;
		while(e>0){
			if((e&1)>0){r*=x;r%=mod;}
			x=(x*x)%mod;
			e>>=1;
		}
		return r;
	}
}
public struct Mint{
	const int mod=(int)1e9+7;
	private long d;
	public Mint(long d){this.d=d;}
	public static implicit operator Mint(long d){return new Mint(d%mod);}
	public static explicit operator long(Mint d){return d.d;}
	public override string ToString(){return d.ToString();}
	public static Mint operator+(Mint a,long b){a.d=(a.d+b)%mod;return a;}
	public static Mint operator+(Mint a,Mint b){a.d=(a.d+b.d)%mod;return a;}
	public static Mint operator-(Mint a,long b){a.d=(mod+a.d-b)%mod;return a;}
	public static Mint operator-(Mint a,Mint b){a.d=(mod+a.d-b.d)%mod;return a;}
	public static Mint operator*(Mint a,long b){a.d=(a.d*b)%mod;return a;}
	public static Mint operator*(Mint a,Mint b){a.d=(a.d*b.d)%mod;return a;}
	public static Mint operator/(Mint a,long b){a.d=(a.d*Mi(b))%mod;return a;}
	public static Mint operator/(Mint a,Mint b){a.d=(a.d*Mi(b.d))%mod;return a;}
	private static long Mi(long a){
		a=(a+mod)%mod;
		long b=mod,u=1,v=0;
		while(b>0){
			long t=a/b;
			a-=t*b;a^=b;b^=a;a^=b;
			u-=t*v;u^=v;v^=u;u^=v;
		}
		u%=mod;
		if(u<0){u+=mod;}
		return u%mod;
	}
}
public class Cb{
	private const int mod=(int)1e9+7;
	public long[] r;
	public Cb(int n){
		r=new long[n];
		r[0]=1;
		for(int i=1;i<n;i++){r[i]=(r[i-1]*i)%mod;}
	}
	public long C1(long n,long k){return (r[n]*Mi(r[k]*r[n-k]))%mod;}
	public long C2(long n,long k){
		long l=1;
		n%=mod;
		for(int i=1;i<=k;i++){l=(l*(n-i+1))%mod;l=(l*Mi(i))%mod;}
		return l;
	}
	public long P1(long n,long k){return n<k?0:(r[n]*Mi(r[n-k]))%mod;}
	public long Mi(long a){
		a=(a+mod)%mod;
		long b=mod,u=1,v=0;
		while(b>0){long t=a/b;a-=t*b;a^=b;b^=a;a^=b;u-=t*v;u^=v;v^=u;u^=v;}
		u%=mod;
		if(u<0){u+=mod;}
		return u%mod;
	}
}
public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public double[] Da2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),double.Parse);}}
	public double[] Da3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),double.Parse);}
	public double[] Da3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),double.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}