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: Accepted)

import math

MOD = 10**9+7
fact = [1]
for i in range(1, 2*10**5+10):
    fact.append((fact[i-1]*i)%MOD)

def comb(n, k):
    ans = 1
    for i in range(k):
        ans = (ans*(n-i))%MOD
    return (ans*pow(fact[k], MOD-2, MOD))%MOD

n, a, b = map(int, input().split())
ans = 1
x = 2
y = n
while y != 0:
    if y%2 != 0:
        ans = (ans*x)%MOD
    x = (x*x)%MOD
    y >>= 1
ans = (ans - comb(n, a) - comb(n, b) -1)%MOD
print(ans)