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>
typedef long long ll;
#define mod 1000000007

ll pow(ll n){
    ll ans = 2;

    for(ll i = n; i > 1; i--){
        ans = (ans*2)%mod;
    }
    return ans;
}

ll combination(ll n,ll r){
    

    if(n < 0||r<0||n<r){
        return 0;
    }

    if(n==r||!r){
        return 1;
    }

    /*if(dp[n][r]){
        return combination(n,r);
    }*/

    
    
    return combination(n-1,r)%mod+combination(n-1,r-1)%mod;
}

int main(void){
    ll n,a,b;
    scanf("%lld %lld %lld",&n,&a,&b);

    

    ll temp = pow(n)-combination(n,a)-combination(n,b)-1;

    printf("%lld\n",temp);

    return 0;
}