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)

#define mod 1000000007
char buf[99];sz;
char out[10];osz=10;
int N,A,B;
long p(long a,long b){
	long ret=1;
	while(b)
	{
		if(b&1)ret=ret*a%mod;
		b>>=1;
		a=a*a%mod;
	}
	return ret;
}
main()
{
	read(0,buf,99);
	for(;;)
	{
		char c=buf[sz++];
		if(c<'0')break;
		N=N*10+c-'0';
	}
	for(;;)
	{
		char c=buf[sz++];
		if(c<'0')break;
		A=A*10+c-'0';
	}
	for(;;)
	{
		char c=buf[sz++];
		if(c<'0')break;
		B=B*10+c-'0';
	}
	long ans=p(2,N)-1;
	long x=1,y=1;
	for(int i=1;i<=A;i++)
	{
		x=x*(N-i+1)%mod;
		y=y*i%mod;
	}
	ans-=x*p(y,mod-2)%mod;
	for(int i=A+1;i<=B;i++)
	{
		x=x*(N-i+1)%mod;
		y=y*i%mod;
	}
	ans-=x*p(y,mod-2)%mod;
	while(ans<0)ans+=mod;
	do{
		out[--osz]=ans%10+'0';
	}while(ans/=10);
	write(1,out+osz,10-osz);
}