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: Accepted)

#include <stdio.h>
#define ll long long

ll MOD = 1000000007;

ll pow2(ll a, ll b){
    ll ret = 1;
    while(b > 0){
        if(b%2 == 1){
            ret = ret*a%MOD;
        }
        a = a*a%MOD;
        b /= 2;
    }
    return ret;
}

ll mul(int s, int e){
    ll ret = 1;
    for(int i = s; i <= e; i++){
        ret = ret*i%MOD;
    }
    return ret;
}

ll fact(int n){
    return mul(1, n);
}

ll nCr(int n, int r){
    return mul(n-r+1, n) * pow2(fact(r), MOD-2) % MOD;
}


int main(void)
{
    int n, a, b;
    scanf("%d %d %d", &n, &a, &b);
    ll ans = (pow2(2, n) - 1 + MOD - nCr(n, a) + MOD - nCr(n, b)) % MOD;
    printf("%d\n", ans);
    return 0;
}