Prime Permutations

Problem code: PPERM

All submissions for this problem are available.

A permutation of N distinct integers between 1 and N, both inclusive, is called a prime permutation of size N iff - for all i between 1 and N, the following condition holds:

The ith integer is the Xth smallest integer in the first i integers, where X is either 1 or a prime number.

Your task is to find out how many prime permutations are there of size N.

Input

The first line contains a single integer T, denoting the number of test cases. Then T lines follow, each containing a single integer N.

Output

For each test case, output a single line containing the number of prime permutations of size N. Since the answers can be very large, output each answer modulo 1,000,000,007.

Example

Input:
4
1
2
3
4

Output:
1
2
6
18

Constraints:

1 ≤ T ≤ 500,000
1 ≤ N ≤ 5,000,000
Each input file will not be larger than 4 MB (4,000,000,000 bytes) in size.

WARNING! Large I/O files. Use fast I/O methods.

Author: yellow_agony
Tester: gamabunta
Editorial http://discuss.codechef.com/problems/PPERM
Date Added: 7-06-2012
Time Limit: 5 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, FORT, FS, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, NODEJS, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TCL, TEXT, WSPC


Comments

some more testcases please

code_jack @ 24 Sep 2012 01:37 AM
some more testcases please

for 5000000 its :- 965379749

code_jack @ 24 Sep 2012 01:44 AM
for 5000000 its :- 965379749 ??

more test cases plsss

anick_gemini @ 24 Sep 2012 04:03 AM
more test cases plsss

please make the solution to

the_c0der @ 11 Oct 2012 10:14 AM
please make the solution to this problem public

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