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 Python (3.4.3) (judge verdict: Runtime Error)

import math


class Comb:
    m_vals = []
    _mod = 1_000_000_007
    _mod2 = 1_000_000_005

    def __init__(self, n: int, r: int):
        m_ls = [1] * (r + 1)

        for i,j in zip(range(n, 0, -1), range(1, r+1)):
            m_ls[j] = (m_ls[j-1]*i * pow(j, self._mod2, self._mod)) % self._mod

        self.m_vals = m_ls

    def vv(self, x):
        return self.m_vals[x]


def main():
    n, a, b = map(int, input().split())
    _mod = 1_000_000_007
    cmb = Comb(n,b)
    all = pow(2,n, _mod) -1
    ans = all + (_mod - cmb.vv(a)) + (_mod - cmb.vv(b))
    ans %= _mod

    print(ans)


main()