2013/quals/find_the_min.md

After sending smileys, John decided to play with arrays. Did you know that
hackers enjoy playing with arrays? John has a zero-based index array, **m**,
which contains **n** non-negative integers. However, only the first **k**
values of the array are known to him, and he wants to figure out the rest.

John knows the following: for each index **i**, where **k** ≤ **i** < **n,
m**[**i**] is the minimum non-negative integer which is *not* contained in the
previous ***k*** values of **m**.

For example, if **k** = 3, **n** = 4 and the known values of **m** are [2, 3,
0], he can figure out that **m**[3] = 1.

John is very busy making the world more open and connected, as such, he
doesn't have time to figure out the rest of the array. It is your task to help
him.

Given the first **k** values of **m**, calculate the **n**th value of this
array. (i.e. **m**[**n** \- 1]).

Because the values of **n** and **k** can be very large, we use a pseudo-
random number generator to calculate the first **k** values of **m**. Given
non-negative integers **a**, **b**, **c** and positive integer **r**, the
known values of **m** can be calculated as follows:

  * **m**[0] = **a**
  * **m**[**i**] = (**b** * **m**[**i** \- 1] + **c**) % **r**, 0 < **i** < **k**

### Input

The first line contains an integer **T** (**T** ≤ 20), the number of test
cases.  
This is followed by **T** test cases, consisting of 2 lines each.  
The first line of each test case contains 2 space separated integers, **n**,
**k** (1 ≤ **k** ≤ 105, **k** < **n** ≤109).  
The second line of each test case contains 4 space separated integers **a**,
**b**, **c**, **r** (0 ≤ **a**, **b**, **c** ≤ 109, 1 ≤ **r** ≤ 109).

### Output

For each test case, output a single line containing the case number and the
**n**th element of **m**.