Number Sequence

1 seconds
64 MB
Medium
LOJ-1065 Udebug Debug
English

Let's define another number sequence, given by the following function:

f(n)={a,if n = 0b,if n = 1f(n1)+f(n2),if n > 1

When a = 0 and b = 1, this sequence gives the Fibonacci sequence. Changing the values of a and b, you will be able to get many different sequences.

Given the values of a, b, you have to find the least m significant digits of f(n).

Input

Input starts with an integer T (≤ 10000), denoting the number of test cases.

Each test case consists of a single line containing four integers a b n m. The values of a and b range in [0,100], value of n ranges in [0, 109] and value of m ranges in [1, 4].

Output

For each case, print the case number and the last m digits of f(n). However, do NOT print any leading zero.

Sample

Sample Input Sample Output

4 0 1 11 3 0 1 42 4 0 1 22 4 0 1 21 4

Case 1: 89 Case 2: 4296 Case 3: 7711 Case 4: 946