Exponentiation Commutativity

Problem code: EXPCOMM

All submissions for this problem are available.

For a given prime number p find the number of all pairs (m, n) of positive integers such that 1 <= m, n <= p*(p-1) and p divides nm - mn. Output the result modulo 1000000007.

Input

The first line contains a single positive integer T <= 100, the number of test cases. T test cases follow. The only line of each test case contains a prime number p , where 2 <= p <= 1012.

Output

For each test case, output a single line containing the answer for the corresponding test case.

Example

Input:
2
2
3

Output:
2
14

Explanation

In the first test required pairs are (1, 1) and (2, 2).

In the second test case required pairs are (1, 1), (1, 4), (2, 2), (2, 4), (3, 3), (3, 6), (4, 1), (4, 2), (4, 4), (4, 5), (5, 4), (5, 5), (6, 3) and (6, 6).

Author: anton_lunyov
Date Added: 3-03-2011
Time Limit: 2 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, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TCL, TEXT, WSPC


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