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<iostream>
using namespace std;

const int MOD = 1000000007;

long long modpow(long long a, long long n, long long mod) {
    long long res = 1;
    while (n > 0) {
        if (n & 1) res = res * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}

// ax + by = gcd(a, b) となるような (x, y) を求める
// 多くの場合 a と b は互いに素として ax + by = 1 となる (x, y) を求める
long long extGCD(long long a, long long b, long long &x, long long &y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    long long d = extGCD(b, a%b, y, x); // 再帰的に解く
    y -= a / b * x;
    return d;
}

// 負の数にも対応した mod (a = -11 とかでも OK) 
inline long long mod(long long a, long long m) {
    return (a % m + m) % m;
}

// 逆元計算 (ここでは a と m が互いに素であることが必要)
long long modinv(long long a, long long m) {
    long long x, y;
    extGCD(a, m, x, y);
    return mod(x, m); // 気持ち的には x % m だが、x が負かもしれないので
}

int main(){
    long long n, a, b;
    long long com1 = 1;
    long long com2 = 1;
    long long nibeki = 1;
    cin >> n >> a >> b;
    nibeki = modpow(2, n, MOD);
    for(long long i = 1; i < a + 1; i++){
        com1 = (((com1 *(n - (i - 1))) % MOD) * modinv(i,MOD)) % MOD;
    }
    com2 = com1;
    for(long long i = a + 1; i < b + 1; i++){
        com2 = (((com2 *(n - (i - 1))) % MOD) * modinv(i,MOD)) % MOD;
    }
    if(nibeki - 1 - com1 - com2 > 0){
        cout << (nibeki - 1 - com1 - com2) % MOD << endl;
    }
    else{
        cout << ((nibeki - 1 - com1 - com2) % MOD) + MOD << endl;
    }
    system("pause");
    return 0;
}