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 Ruby (2.3.3) (judge verdict: Wrong Answer)

ONE = '1'.freeze
def inv(x)
    res = 1 # 逆元をどんどんかけるやつ
    beki = x # 逆元を計算したい値のMOD化でのべき乗
    (MOD - 2).to_s(2).reverse.chars do |digest|
        res = (beki * res) % MOD if digest == ONE
        beki = (beki * beki) % MOD
    end
    res
end

def nCk(n,k)
    res = 1
    for i in 1..k do
        res = res * (n-i+1) * inv(i)
        res %= MOD
    end
    res
end

MOD = 10**9+7
str = gets.split
N,a,b = str[0].to_i, str[1].to_i, str[2].to_i
n = N

answer = 1
c = 2
while n > 0
    d = n % 2
    answer *= d == 1 ? c : 1
    answer %= MOD
    c *= c
    c %= MOD
    n /= 2
end
p answer
answer += MOD - 1
answer %= MOD
answer += MOD - nCk(N,a)
answer %= MOD
answer += MOD - nCk(N,b)
answer %= MOD

puts answer