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 (3.8.2) (judge verdict: Time Limit Exceeded)

def main():
    n, a, b = map(int, input().split())
    mod = 10 ** 9 + 7 #素数
    
    def modpow(x, n, mod):
        res = 1
        while n:
            if n % 2:
                res *= x % mod
            x *= x % mod
            n >>= 1
        return res
    
    def cmb(n, r, mod):
        # 分子(n*(n-1)*...*(n-r+1))
        nume = 1
        for i in range(n-r+1, n+1):
            nume = nume * i# % mod
        # 分母（1*2*...*r）
        deno = 1
        for j in range(1, r+1):
            deno = deno * j % mod
        d = modpow(deno, mod-2, mod)
        return nume * d % mod
    
    all_cmb = pow(2, n, mod) - 1
    bad_a = cmb(n, a, mod)
    bad_b = cmb(n, b, mod)    
    print((all_cmb-bad_a-bad_b) % mod)

if __name__ == '__main__':
    main()