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<math.h>

long kai(long);

int main(void){
  int n, a, b; 
  long bou, com = 0;
  int i;
  
  scanf("%d %d %d", &n, &a, &b);
  
  for(i = 1; i <= n; i++){
    if(i == a || i == b)  continue;
    com += kai(n) / (kai(i) * kai(n-i));
  }
  
  bou = com % (long)(pow(10, 9) + 7);
  
  if(com == 0)  printf("0\n");
  else  printf("%d\n", bou);
  
  return 0;
}

long kai(long x){
  int i;
  long result = 1;
  
  for(i = 1; i <= x; i++)  result *= i;
  
  return result;
}