Twins

HOLIDAYS ARE COMING!

Last day of the advanced algorithmic classes and two siblings are walking in a big corridor. But one of the twins asks his brother: “Do you know in how many ways we can walk through this corridor?”

The corridor is $L$ meters long and it is represented as a $2 \times L$ grid. Initially, twin $A$ is at $(1,1)$ and twin $B$ is at $(2,1)$ , and they set the rules to move along the corridor:

A twin can move to the left tile $(+1,0)$ .
A twin can advance to the tile in front $(0,+1)$ .
A twin can cross in a diagonal, e.g. $(+1,+1)$ or $(-1,+1)$ .
The destination tiles must exist.
Both move at the same time.
They always move while they are not in the last tiles $(1,L)$ or $(2,L)$ .
They finish when both are in any of the last tiles $(1,L)$ or $(2,L)$ .

For a given $L > 1$ , return the number of of ways in which the twins can walk through the corridor. Because this number could be very large, return the result modulo $10^9 + 7$ .

Input

The input starts with the number of test cases $T \leq 1000$ . For each test case, there is an integer $L \leq 10^6$ representing the length of the corridor.

Output

For each test case, output an integer on a single line representing the number of ways in which the twins can walk through the corridor, modulo $10^9 + 7$ .

In the first example there are 8 combinations:

$A = (1,2)$ and $B = (1,2)$
$A = (1,2)$ and $B = (2,2)$
$A = (2,2)$ and $B = (1,2)$
$A = (2,2)$ and $B = (2,2)$
$A = (2,1)$ and $B = (1,2) \rightarrow A = (2,2)$ and $B = (1,2)$
$A = (2,1)$ and $B = (1,2) \rightarrow A = (1,2)$ and $B = (1,2)$
$A = (2,1)$ and $B = (2,2) \rightarrow A = (2,2)$ and $B = (2,2)$
$A = (2,1)$ and $B = (2,2) \rightarrow A = (1,2)$ and $B = (2,2)$

Problem information

Author: Javier Segovia

Generation: 2026-01-25T22:01:36.713Z