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Calculate the number of solutions of the equation x*y=N! . As the answer might be very large, give your output modulo 1000007.
The first line of input contains an integer T (1<=T<=5) – the number of test cases.
The next T lines contain an integer N (1<=N<=100000).
Output an integer, the answer for each test case, modulo 1000007 on a separate line.
Sample Test Cases
Input 1 3 Output 4 Input 2 2 500 Output 2 382728
For the first test case, 3! = 6 which can be expressed as 1*6 , 6*1, 2*3 and 3*2.
NOTE: x=1, y=6 and x=6, y=1 are considered separate solutions. Similarly for all other solutions as well.
|Time Limit:||1 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP14, JAVA, PYTH, PYTH 3.6, 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, PYP3, CLOJ, FS|
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