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: Accepted)

N,a,b = [int(i) for i in input().split()]
mod = 10**9+7
def power(x, n):
    ans = 1
    while(n > 0):
        if(bin(n & 1) == bin(1)):
            ans = ans*x%mod
        x = (x*x)%mod
        n = n >> 1 #ビットシフト
    return ans
def fact(m, n):
    val = 1
    for i in range(m, n+1):
        val = val*i % mod
    return val
    
def cmb1(N, r):
    A = fact(N-r+1, N)%mod
    B = fact(1, r)%mod
    return A, B, (A*power(B, mod-2))%mod
def cmb2(a, b, A, B):
    A = fact(N-a+1, N-b)*A%mod
    B = fact(b+1, a)*B%mod
    return (A*power(B, mod-2))%mod
if(a>N//2):
    a = N-a
if(b>N//2):
    b = N-b
tmp = max(a,b)
b = min(a,b)
a = tmp
A, B, K1 = cmb1(N, b)
K2 = cmb2(a, b, A, B)
print((power(2, N)-1-K1-K2)%mod)