RECEQU - Recurrence Equation Finder

Many problems have solutions involving linear recurrence equations of the form f(n) = a · f(n-1) + b · f(n-2) (n ≥ 2). Usually the coefficients a and b are between 0 and 10, so it would be useful to have a program which checks if some given values can be produced by such a recurrence equation. Since the growth of the values f(n) can be exponential, we will consider the values modulo some integer constant k.

More specifically you will be given f(0), f(1), k and some value pairs (i , xi), where xi is the remainder of the division of f(i) by k.

You have to determine coefficients a and b for the recurrence equation f such that for each given value pair (i, xi) the equation xi = f(i) mod k holds.

Hints

You can write the recurrence equation as follows:
<pre>
(a b) (f(n-1)) =( f(n) )
(1 0) (f(n-2))  (f(n-1))
</pre>

Let <pre>
      (a b)
A :=  (1 0)
</pre>

Then, A<sup>n</sup> · (f(1),f(0))<sup>T</sup> = (f(n+1),f(n))<sup>T</sup>. These equations also apply if everything is calculated modulo k. To speed up the calculation of An, the identity An = (An div 2)2 · An mod 2 may be used. Also, (a · b) mod c = ((a mod c) · (b mod c)) mod c.

Input

The first line of the input contains a number T ≤ 20 which indicates the number of test cases to follow.

Each test case consists of 3 lines. The first line of each test case contains the three integers f(0), f(1) and k, where 2 ≤ k ≤ 10000 and 0 ≤ f(0),f(1) < k. The second line of each test case contains a number m ≤ 10 indicating the number of value pairs in the next line. The third line of each test case contains m value pairs (i,xi), where 2 ≤ i ≤ 1000000000 and 0 ≤ xi < k.

Output

For each test case print one line containing the values a and b separated by a space character, where 0 ≤ a,b ≤ 10. You may assume that there is always a unique solution.

Example

Input:
2
1 1 1000
3
2 2 3 3 16 597
0 1 10000
4
11 1024 3 4 1000000000 4688 5 16

Output:
1 1
2 0

Added by:Adrian Kuegel
Date:2007-01-18
Time limit:1.436s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET

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