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: Time Limit Exceeded)

#include<stdio.h>
#include<math.h>
int count=0;
int mod_pow(int x,int n,int p){
	int ret=1;
	while(n>0){
		if(n&1){
			ret*=x;
			ret%=p;
		}
		x*=x;
		x%=p;
		n>>=1;
	}
	return ret;
}
int combination(int n, int r)
{
	if (r == 0 || r == n)
	return (1);
	else if (r == 1)
	return (n);
	return (combination(n - 1, r - 1) + combination(n - 1, r));
}
int main(){
	int n,a,b;
	scanf("%d",&n);
	scanf("%d",&a);
	scanf("%d",&b);
	int A=mod_pow(2,n,1000000007)-1;
	A-=combination(n,a);
	A-=combination(n,b);
	printf("%d",A);
}