DETER  Find The Determinant
In this problem you have to calculate the determinant of an N x N matrix whose entries are given by m[i][j] = gcd(i,j), 1 ≤ i,j ≤ N.
Here gcd(i,j) denotes the greatest common divisor of i and j.
As the determinant D can grow very large, you have to print D%1000003.
Input
First line of input consists of a single integer containing the number of test cases T ( equal to around 500000), each of the following T lines contain an integer N the size of the matrix. N lies between 1 and 2000000 ( both inclusive ).
Output
One line corresponding to each test case containing the determinant modulo 1000003 for the corresponding test case.
Example
Input: 3 1 3 5 Output: 1 2 16
hide comments
BugsBunny :):
20111129 19:58:01
:( 

[Trichromatic] XilinX:
20090410 03:28:19
This problem is moved to tutorial section because a similar (almost the same) problem MSE08H is available in the classical section. 

Ajay Somani:
20090331 15:59:01
second. 

~!(*(@*!@^&:
20090318 17:03:27
In which book? 1st, 2nd ...? 
Added by:  Ajay Somani 
Date:  20070901 
Time limit:  1s 
Source limit:  2048B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  "The Art Of Computer Programming" 