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: Runtime Error)

#include<stdio.h>
int r[100000000]={0};
int bouquet(int n,int a,int b){
	if(n==1)r[0]=1;
	else{
		bouquet(n-1,0,0);
		for(int i=n;i>0;i--){
			r[i]+=r[i-1];
		}
		r[0]++;
		if(a){
			int count=0;
			for(int i=0;r[i]>0&&i<n;i++){
				if(i!=a-1&&i!=b-1){
					count+=r[i];
				}
				count=count%1000000007;
			}
			return count;
		}
	}
}
int main(){
	int n,a,b;
	scanf("%d",&n);
	scanf("%d",&a);
	scanf("%d",&b);
	printf("%d",bouquet(n,a,b));
}