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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MOD = 1e9+7;

ll modpow(ll a, ll b , ll mod){
  if(b == 0) return 1;
  ll res = modpow(a, b/2, mod);
  if(b%2){
    res = res * res % mod;
    res = res * a % mod;
  }else {
    res = res * res % mod;
  }
  return res;
}

ll nCk(ll n, ll k){
  ll x = 1;
  ll y = 1;
  for(ll i = 0;i < k;i++){
    x= x*(n-i)%MOD;
    y= y*(i+1)%MOD;
  }
  //cout<<MOD<<" "<<n<<" "<<k<<" "<<x<<" "<<y<<endl;
  return (x*modpow(y, MOD-2, MOD)%MOD);
}

int main(){
  ll n, a, b;
  scanf("%lld%lld%lld", &n, &a, &b);
  ll ans = modpow(2, n, MOD);
  //cout<<nCk(n, a)<<" "<<nCk(n, b)<<endl;
  ans= (ans - nCk(n, a) - nCk(n, b))% MOD;

  printf("%lld\n", ans -1);
  return 0;
}