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;
using ll = long long;

int base = 1e9 + 7;

ll invmod(ll p, ll q) {
  ll r = 1;
  while (q) {
    if (q&1) r = (r*p) % base;
    p = p*p % base;
    q >>= 1;
  }
  return r;
}

ll combimod(ll n, ll m) {
  ll t = 1;
  while (m) {
    t = t * n % base;
    t = t * invmod(m, base-2) % base;
    n--; m--;
  }
  return t;
}

int main() {
  ll n, a, b; cin >> n >> a >> b;
  
  ll total = invmod(2, n) - 1;
  total = (total + base - combimod(n, a)) % base;
  total = (total + base - combimod(n, b)) % base;
  
  cout << total << endl;
}