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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

#!/usr/bin/env python3
import sys

MOD = 1000000007  # type: int

class ModOperator:
    def __init__(self, MOD: int = 10 ** 9 + 7):
        self.MOD = MOD
        self.factorials = [1, 1]    # 階乗のメモ

    # x^n % MOD
    def mod_pow(self, x: int, n: int):
        bi = str(format(n, "b"))
        res = 1
        a = x
        for i in range(len(bi)):
            if n >> i & 1:
                res = (res * a) % self.MOD
            a = (a * a) % self.MOD
        return res
    
    # x! % MOD
    def mod_fact(self, x: int):
        if x < len(self.factorials):
            return self.factorials[x]
        else:
            res = self.factorials[-1]
            for i in range(len(self.factorials), x + 1):
                res = res * i % self.MOD
                self.factorials.append(res)
        return res % self.MOD

    # inverse of a number
    def mod_inv(self, x: int):
        return self.mod_pow(x, self.MOD - 2)
    
    # conmination nCk
    def mod_comb(self, n: int, k: int):
        numerator = self.mod_fact(n)
        denomintator1 = self.mod_fact(k)
        denomintator2 = self.mod_fact(n - k)
        denomintator = denomintator1 * denomintator2 % self.MOD
        return numerator * self.mod_inv(denomintator) % self.MOD


def main():
    n, a, b = map(int, input().split())
    op = ModOperator()
    print((op.mod_pow(2, n) - op.mod_comb(n, a) - op.mod_comb(n, b) - 1) % MOD)

    return


if __name__ == '__main__':
    main()