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)

import sys
input = sys.stdin.readline

def main():
    def calc(n, mod):
        f = 1
        for m in range(1, n + 1):
            f *= m
            f %= mod
        fn = f
        inv = pow(f, mod - 2, mod)
        invs = [1] * (n + 1)
        invs[n] = inv
        for m in range(n, 1, -1):
            inv *= m
            inv %= mod
            invs[m - 1] = inv 
        return fn, invs

    mod = 10**9+7 
    n,a,b=map(int,input().split())
    ans=0
    fn,invs=calc(n,mod)
    for i in range(1,n+1):
        if i==a or i==b:
            continue
        else:
            ans+=(fn*invs[i]*invs[n-i])%mod
    print(ans)

if __name__ == '__main__':
    main()