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>
#include <stdlib.h>
int main(){
  int N,a,b,i,j,k,com2,com3;
  int sum=0;
  int com1=1;
  scanf("%d %d %d",&N,&a,&b);
  for(i=1;i<N+1;i++) com1=com1*i;
  for(i=1;i<N+1;i++){
    if(i==a || i==b) continue;
    com2=1;
    com3=1;
      for(j=2;j<i+1;j++){
        com2=com2*j;
    }
    for(k=2;k<N-i+1;k++){
      com3=com3*k;
    }
    sum=(sum+com1/com2/com3)%1000000007;
  }
  printf("%d",sum);
  return 0;
}