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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>

long long mo=1e9+7;

long long doing(long long num1,long long num2)
{
	long long keep=1;
	num1=num1%mo;
	while (num2)
	{
		if (num2&1)
		{
			keep=keep*num1%mo;
			num2--;
		}
		num2=num2/2;
		num1=num1*num1%mo;
	}
	return keep;
}

long long quick(long long num1,long long num2)
{
	if (num2>num1) return 0;
	long long keep=1;
	int i;
	for (i=1;i<=num2;i++)
	{
		long long x=(num1+i-num2)%mo;
		long long y=i%mo;
		keep=keep*(x*doing(y,mo-2)%mo)%mo;
	}
	return keep;
}

long long lucas(long long num1,long long num2)
{
	if (num2==0) return 1;
	else return quick(num1%mo,num2%mo)*lucas(num1/mo,num2/mo)%mo;
}


int main()
{
	long long n,a,b;
	scanf("%lld%lld%lld",&n,&a,&b);
	long long answer;
	answer=doing(2,n)-1-lucas(n,a)-lucas(n,b);
	while (answer<0) answer=answer+mo;
	printf("%lld",answer);
	return 0;
}