Tree Expectancy

All submissions for this problem are available.
Read problems statements in Mandarin Chinese, Russian and Vietnamese as well.
Consider an ordered tree with N vertices. Your task is to calculate the expected value of the number of vertices having exactly one child in such tree assuming that it is uniformly chosen from the set of all ordered trees of size N.
Input
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
Each testcase contains a single integer N for which you should calculate the answer.
Output
For each test case, output a single line containing two integers, which are explained below.
Consider the answer to be a proper fraction P/Q, where gcd(P, Q) = 1. Then your task is to output two integers PQ^{1} mod 10^{9}+7 and PQ^{1} mod 10^{9}+9.
Constraints
 1 ≤ T ≤ 10^{5}
 It is guaranteed that Q will be invertible with respect to both the modulos.
Subtasks
Subtask #1 (10 points)
 1 ≤ N ≤ 10^{3}
Subtask #2 (20 points)
 1 ≤ N ≤ 10^{6}
Subtask #3 (30 points)
 1 ≤ N ≤ 10^{9}
Subtask #4 (40 points)
 1 ≤ N ≤ 10^{18}
Example
Input: 4 1 2 3 4 Output: 0 0 1 1 1 1 400000004 200000003
Explanation
You can see every possible tree with 1, 2, 3 or 4 vertices on the diagram below.
From this you can see that answers for these inputs are 0/1 = 0, 1/1 = 1, (2+0)/2 = 1 and (3+1+1+1+0)/5 = 6/5 correspondingly.
Author:  melfice 
Editorial  https://discuss.codechef.com/problems/EXPTREE 
Tags  combinatorics, july17, math, melfice, numbertheory 
Date Added:  27062017 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.5, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, SCM chicken, CLOJ, FS 
Comments
 Please login at the top to post a comment.
SUCCESSFUL SUBMISSIONS
Fetching successful submissions
HELP
If you are still having problems, see a sample solution here. 