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: Wrong Answer)

n, a, b = map(int, input().split())
a, b = min(a, n-a), min(b, n-b)
ans = pow(2, n, 1000000007) - 1

temp1, temp2, count = 1, 1 ,0
for i in range(min(a, b)):
    temp1 *= n - i
    temp2 *= i + 1
    if temp1 >= 1000000007:
        temp1 %= 1000000007
        count += 1
if a == b:
    ans -= 2 * (temp1 + (100000007 * count) // temp2) % 1000000007
    if ans < 0:
        print(ans + 1000000007)
    else:
        print(ans)
else:
    ans -= (temp1 + (100000007 * count) // temp2) % 1000000007
    if ans < 0:
        ans += 1000000007
    for i in range(min(a, b), max(a, b)):
        temp1 *= n - i
        temp2 *= i + 1
        if temp1 >= 1000000007:
            temp1 %= 1000000007
            count += 1
    ans -= (temp1 + (100000007 * count) // temp2) % 1000000007
    if ans < 0:
        print(ans + 1000000007)
    else:
        print(ans)