github.com/captn3m0/codechef.git

---
{"languages_supported":{"0":"NA"},"title":"GLASS","category":"NA","old_version":true,"problem_code":"GLASS","tags":{"0":"NA"},"layout":"problem"}
---

<h3> All submissions for this problem are available. </h3><h3> Statement </h3>

<p>
Chef has n glasses each with a capacity of xi. <br />
There are Q+1 people playing a game including the Chef himself. Everyone at his/her turn gives a positive integer M<sub>i</sub> and asks the Chef if volume M of water can be transferred using the n glasses with Chef. Chef at his own turn wants to give M as the highest integer volume which cannot be constructed using these n glasses. <br />
So, you need to help chef with this game. <br />
Assume that to construct a volume M, we have a reserve with infinite volume of liquid. If Chef uses i<sup>th</sup> glass, he has to transfer a volume equal to xi in one turn. He can use a glass multiple times. However, transfer of liquid between glasses is not permitted. For example, you cannot obtain volume of 2 by tranferring liquid from glass of volume 5 to glass of volume 3. <br />
It is always possible to construct volume 0.
</p>

<h3> Input </h3> 
First line contains t ( ≤ 20 ) which is the number of test cases. For each test case, the first line contains n ( the number of glasses ) . The next line contains n space separated integers denoting the capacity of each glass. The next line contains a single integer Q - the number of players excluding the Chef. Then follows a line containing 3 space separated integers a,b,c. Calculate M<sub>i</sub> for the ith person as (a*i+b)%c ( i ≥ 1 ). 
<h3> Output </h3> 

For each test case, the first line of output should contain the highest value M desired by Chef [ If there is no positive M, then output -1 ]. Then follows a line containing 2 integers A and B where A denotes the number of M<sub>i</sub> which cannot be constructed using the given glasses and B denotes the number of M<sub>i</sub> which can be constructed.

<h3> Sample Input </h3> 

<pre>
1
2
3 5
2
8 1 10

</pre>

<h3> Sample Output </h3>

<pre>
7
1 1
</pre>

<h3> Constraints </h3>
<p>
1 &lt; n ≤ 10 <br />
1 ≤ xi ≤ 10<sup>7</sup> <br />
MIN(xi) ≤ 100000 <br />
1 ≤ Q ≤ 1000000 <br />
1 ≤ a,c ≤ 10<sup>12</sup> <br />
0 ≤ b ≤ 10<sup>12</sup> <br />
</p> 
<br />
<h3> Sample Test Case Explanation </h3>
<p> 
There are 2 glasses of size 3 and 5. Volumes 1, 2, 4, 7 cannot be created by the combinations of glass suggested in the problem. Hence, the highest volume is 7. <br />
The 2 queries are for 9 and 7. 9 can be created using the glasses and 7 cannot. 
</p>