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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define REP(i,n) for(ll i=0, i##_len=(n); i<i##_len; ++i)
#define REPR(i,n) for(ll i = n;i >= 0;--i)
#define FOR(i,m,n) for(ll i = m, i##_len=(n);i <i##_len; ++i)
#define all(x) (x).begin(),(x).end()
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
const int INF = 1e9;
const ll LLINF = 1e16;
 
ll modinv(ll a, ll m) {
    ll b = m, u = 1, v = 0;
    while (b) {
        ll t = a / b;
        a -= t * b; swap(a, b);
        u -= t * v; swap(u, v);
    }
    u %= m;
    if (u < 0) u += m;
    return u;
}

ll RepeatSquaring(ll N, ll P, ll M){
    if(P==0) return 1;
    if(P%2==0){
        ll t = RepeatSquaring(N, P/2, M);
        return t*t % M;
    }
    return N * RepeatSquaring(N, P-1, M);
}

ll mod_conv(ll n,ll r,ll mod)
{
    ll nume = 1;
    ll deno = 1;

    FOR(i,0,r){
        nume = (nume  * (n - i)) % mod;
        deno = (deno * (1 + i)) % mod;
    }

    return (nume * modinv(deno,mod))%mod;
}

int main(void)
{
    ll n;
    ll mod = 1e9 + 7;
    cin >> n;
    ll all = RepeatSquaring(2, n, mod) - 1;
    ll a, b;
    cin >> a >> b;

    ll ans = all - mod_conv(n, a,mod);
    ans = (ans < 0) ? ans + mod : ans;

    ans = ans - mod_conv(n, b, mod);
    ans = (ans < 0) ? ans + mod : ans;
    

    if(n <= 2){
        cout << 3/0 << endl;
    }
    else{
        cout << ans << endl;
    }

    return 0;
}