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>
#include <iostream>
#include <cstdio>
#include <iomanip>
using namespace std;
using P = pair<int,int>;
typedef long long ll;


#define rep(i,n) for (int i=0; i<(n); i++)
const int INF =1001001001;
const ll BIG = 1000000007;
const double PI = 3.141592653589793;

ll modpow(ll a, ll b, ll mod = 1000000007) {
    ll res = 1;
    for(a %= mod; b; a = a * a % mod, b>>=1) if(b&1) res = res*a%mod;
    return res;
}

ll combination_nCa(ll n, ll r, ll mod=1000000007){
    ll x = 1, y = 1;
    rep(i,r){
        x = (x*(n-i))%mod;
        y = (y*(i+1))%mod;
    }
    return (x*modpow(y, mod-2))%mod;
}

int main(){
    ll n, a, b;
    cin >> n >> a >> b;
    ll ans = modpow(2, n) - 1 - combination_nCa(n, a) - combination_nCa(n, b);
    if(ans<0) ans += BIG;
    cout << ans << endl;
    return 0;
}