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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
using namespace std;

int kaizyou(int x,int y);
int main(){
    int N=0;
    int a=0;
    int b=0;
    int result=0;
    cin >> N >> a >> b;
   for(int i=1;i<=N;i++){
       if((i==a)||(i==b)){
           continue;
       }else{
           result+=kaizyou(N,i)/kaizyou(i,i);
       }
   }
   cout << result << endl;
}
int kaizyou(int x,int y){
    int point=x;
    int result=1;
    for(int i=1;i<point+1;i++){
        result*=x;
        x--;
        if (i==y){
            break;
        }
    }
    return result;
}