john-and-the-ladder-of-odds-1

This weekend John is headed to visit the new fun city in town. A very popular game is called the "Ladder of odds".

In this game, you have to climb up the ladder of height h, using only odd number of steps. But you don't progress to the next level unless you climb down as well..!!!

For example: If we have a ladder of height 4 we can go up in 3 ways (1 + 1 + 1 + 1, 3 + 1, 1 + 3) .

Being the curious kid that John is, he would like to know the total number of ways to do so. 

Moreover, the entire place contains these game ladders of varying heights up to N.

So, the 1st game has h = 1, the 2nd game has h = 2, and so on upto the Nth game.

Determine the summation of number of ways to complete each game if a new game can only be started after completion of previous game.

Input:

The first line contains number of test cases, T. Each of the following T lines contain an integer N, as defined above.

Output:

Each line of output should contain exactly one number indicating answer of corresponding test case. Output may be too large so print it modulo 10^9+9.

Constraints:

1 ≤ T ≤ 100000 
1 ≤ N ≤ 10^15

SAMPLE INPUT
3
1
2
3

SAMPLE OUTPUT
1
2
6

Source: hackerearth | Difficulty: MEDIUM
Tags: Matrices


Solutions: