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.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;


class Program {

	static int testN=3;
	static long mod = 1000000007;
	//static long mod =998244353; 
	static System.IO.StringReader sr;
	static void Main(string[] args) {
		char[] cs = new char[] { ' ' };
		//char[] cs = new char[] { ' ', ',' };

		//int n = int.Parse(Console.ReadLine());
		//int val = int.Parse(Console.ReadLine());
		//int[] vals = parseAry(Console.ReadLine().Split(cs));
		//string str = Console.ReadLine();
		//string[] strs = Console.ReadLine().Split(cs);

		//string res = "";
		long res = long.MaxValue; ;


		int[] vals = parseAry(Console.ReadLine().Split(cs));
		long n=vals[0];

		long all = mod_pow(2, n);
		all -= combination(n, vals[1]);
		all -= combination(n, vals[2]);

		all--;
		all %= mod;
		if ( all < 0 ) { all += mod; }
			Console.WriteLine(all);

		return;

	}


	static long combination(long n, long r) {
		if ( r * 2 > n ) r = n - r;
		long dividend = 1;
		long divisor = 1;
		for ( long i = 1; i <= r; ++i ) {
			dividend *= ( n - i + 1 );
			dividend %= mod;

			divisor *= i;
			divisor %= mod;
		}

		return (dividend * mod_pow(divisor, mod - 2)) % mod;
	}

	static public long mod_pow(long x, long n) {
		long mod = 1000000007;
		long res = 1;
		while ( n > 0 ) {
			if ( ( n & 1 ) == 1 ) { res = res * x % mod; }
			x = x * x % mod;
			n >>= 1;
		}
		return res;
	}

  


	//	文字列strをindex番目からdで上書き
	static string strOverWrite(string str, int i, string s) {
		return str.Remove(i, s.Length).Insert(i, s);
	}

	//　String[]  ----->  int[]
	static int[] parseAry(string[] str) {
		int[] nums = new int[str.Length];
		for ( int i = 0; i < str.Length; i++ ) { nums[i] = int.Parse(str[i]); }
		return nums;
	}
	//　String[]  ----->  long[]
	static long[] parseAryL(string[] str) {
		long[] nums = new long[str.Length];
		for ( int i = 0; i < str.Length; i++ ) { nums[i] = long.Parse(str[i]); }
		return nums;
	}

	//文字列を1文字ずつString[]に入れる
	static string[] strAry(String str) {
		string[] re = new string[str.Length];
		for ( int i = 0; i < str.Length; i++ ) { re[i] = str[i].ToString(); }
		return re;
	}



}