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 Lua (Lua 5.3.5) (judge verdict: Accepted)

local mod=1000000007

local function bmul(x,y)
    return (x*y)%mod
end

local function badd(x,y)
    return (x+y)%mod
end

local function bsub(x,y)
  return x<y and x-y+mod or x-y
end

local function bmod(x)
    x=tostring(x)
    local ten=10
    local cry=1
    local xod=0
    for i=#x,1,-1 do
        local xub=tonumber(x:sub(i,i))
        xod=(xod+xub*cry)%mod
        cry=(cry*ten)%mod
    end
    return xod
end

local function bpow(x,y)
    x=bmod(x)
    y=bmod(y)
    local xpy=1
    while 0<y do
        if y%2==1 then
            xpy=bmul(xpy,x)
            y=y-1
        end
        x=bmul(x,x)
        y=y//2
    end
    return xpy
end

local function comb(x,y)
    local xyi=1
    local yii=1
    for i=1,y do
        xyi=bmul(xyi,x+1-i)
        yii=bmul(yii,i)
    end
    return bmul(xyi,bpow(yii,mod-2))
end

local n,a,b=io.read("n","n","n")
local total=bpow(2,n)-1
local comba=comb(n,a)
local combb=comb(n,b)
print(bsub(total,badd(comba,combb)))