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: Accepted)

N,A,B=$<.read.split.map(&:to_i)
require 'openssl'
MOD=10**9+7

def pow(a,b,mod)
    a.to_bn.mod_exp(b.to_bn,mod).to_i
    # res = 1
    # while 0 < b
    #     res = res * a % mod if b & 1 == 1
    #     a = a * a % mod
    #     b >>= 1
    # end
    # res
end

def inv(a,mod)
    pow(a,mod-2,mod)
end

def comb(a,b,mod)
    x = (a-b+1..a).inject(1) {|n,x| n*x%mod }
    y = (1..b).inject(1) {|n,x| n*x%mod }
    x * inv(y,mod) % mod
end

ret = (pow(2,N,MOD) - 1 - comb(N,A,MOD) - comb(N,B,MOD)) % MOD
puts ret