BILLBOARDS

We are starting preparations for Hacker Cup 2013 really early. Our first step 
is to prepare billboards to advertise the contest. We have text for hundreds of 
billboards, but we need your help to design them.

The billboards are of different sizes, but are all rectangular. The billboard 
widths and heights are all integers. We will supply you with the size in inches 
and the text we want printed. We want you to tell us how large we can print the 
text, such that it fits on the billboard without splitting any words across 
lines. Since this is to attract hackers like yourself, we will use a monospace 
font, meaning that all characters are of the same width (e.g.. 'l' and 'm' take 
up the same horizontal space, as do space characters). The characters in our 
font are of equal width and height, and there will be no additional spacing 
between adjacent characters or adjacent rows.

Let's say we want to print the text "Facebook Hacker Cup 2013" on a 350x100" 
billboard. If we use a font size of 33" per character, then we can print 
"Facebook" on the first line, "Hacker Cup" on the second and "2013" on the 
third. The widest of the three lines is "Hacker Cup", which is 330" wide. There 
are three lines, so the total height is 99". We cannot go any larger.


INPUT

The first line of the input file contains a single integer T: the number of 
test cases. T lines follow, each representing a single test case in the form "W 
H S". W and H are the width and height in inches of the available space. S is 
the text to be written.


OUTPUT

Output T lines, one for each test case. For each case, output "Case #t: s", 
where t is the test case number (starting from 1) and s is the maximum font 
size, in inches per character, we can use. The size must be an integral number 
of inches. If the text does not fit when printed at a size of 1", then output 0.


CONSTRAINTS

    1 ≤ T ≤ 20
    1 ≤ W, H ≤ 1000
    The text will contain only lower-case letters a-z, upper-case letters A-Z, 
digits 0-9 and the space character
    The text will not start or end with the space character, and will never 
contain two adjacent space characters
    The text in each case contains at most 1000 characters 


EXAMPLE INPUT

5
20 6 hacker cup
100 20 hacker cup 2013
10 20 MUST BE ABLE TO HACK
55 25 Can you hack
100 20 Hack your way to the cup


EXAMPLE OUTPUT

Case #1: 3
Case #2: 10
Case #3: 2
Case #4: 8
Case #5: 7