題目：

Description

Rikka is poor at math. Now she asks you for help.

A set is known as extraordinary set when the minimum integer of it is equal to its size. 
min{x : x ∈ S}=|S|
For example, S = {3, 7, 8} is extraordinary.

gn is the number of extraodinary subsets of {1, 2, ..., n}.

Rikka wants to know the value of gn

Input

Input consists of one integer n(1 ≤ n ≤ 10^18)

Output

Output a single integer  gn mod1000000009

Sample Input

16

Sample Output

987

思路：

程式碼：

#include<iostream>
using namespace std;

long long a, b, c, d;
long long x1, x2, x3, x4;

void f(long long n)
{
	if (n == 0)
	{
		a = 1;
		b = 0;
		c = 0;
		d = 1;
		return
 
;
	}
	f(n / 2);
	x1 = a*a + b*c;
	x2 = (a + d)*b;
	x3 = (a + d)*c;
	x4 = b*c + d*d;
	a = x1 % 1000000009;
	b = x2 % 1000000009;
	c = x3 % 1000000009;
	d = x4 % 1000000009;
	if (n % 2)
	{
		c += a;
		a = c - a;
		d += b;
		b = d - b;
	}
}

int main()
{
	long long n;
	cin >> n;
	f(n);
	cout << b << endl;
	return 0;
}