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 (3.4.3) (judge verdict: Wrong Answer)

import math


def ncr(n, r):
    r = min(r, n - r)
    if n + r < 4000:
        return math.factorial(n) // math.factorial(n-r) // math.factorial(r)
    if r == 0:
        return 1
    if r == 1:
        return n
    numerator = list(range(n - r + 1, n + 1))
    denominator = list(range(1, r+1))
    for p in range(2, r + 1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p - 1, r, p):
                numerator[k - offset] //= pivot
                denominator[k] //= pivot
    result = 1
    for k in range(r):
        result *= numerator[k]
    return result


n, a, b = map(int, input().split())
MOD = 10**9 + 7
cmb_count = 0
for i in range(n):
    if not(i == a or i == b):
        cmb_count += ncr(n, i)
print(cmb_count % MOD)