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: Accepted)

#include <bits/stdc++.h>
using namespace std;
int n, a[100010];
const int mod = 1e9 + 7;
int qp(int x, int y)
{
    int ans = 1;
    int base = x;
    while (y)
    {
        if (y % 2)
            ans = 1ll * ans * base % mod;
        base = 1ll * base * base % mod;
        y = y / 2;
    }
    return ans;
}

int cc(int x, int y)
{
    int ans = 1;
    for (int i = 1; i <= y; i++)
    {
        ans = 1ll * ans * (x - y + i) % mod * qp(i, mod - 2) % mod;
    }
    return ans;
}
int main()
{
    int n, a, b;
    scanf("%d", &n);
    scanf("%d%d", &a, &b);
    printf("%d\n", (qp(2, n) - 1 - (cc(n, a) + cc(n, b)) % mod + mod) % mod);
    return 0;
}