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 <iostream>//cout<<right で右揃え
#include <iomanip>//cout<<stw(数字) で空白による桁揃え
#include <string>
#include <vector>
#include <algorithm>
#include <cstdlib>//abs()で整数絶対値
#include <cmath>//abs()かfabs()で少数絶対値

using namespace std;

int main(void){
    long n;cin>>n;
    int a,b;cin>>a>>b;
    long ans = 0;
    vector<long> C(n+1);
    C[0] = 1;
    C[1] = n;
    for(long i=2;i<=n;i++){
        if(i<=n/2){
            C[i] = C[i-1]*(n-(i-1))/i;
            C[i] %= 1000000007;
        }else{
            C[i] = C[n-i];
        }
    }
    for(long i=1;i<=n;i++){
        while(1){
            if(i==a||i==b)break;
            ans += C[i];
            ans %= 1000000007;
            break;
        }
    }
    cout << ans << endl;
    return 0;
}