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. If you print
a word on one line and print the next word on the next line, you do not need
to print a space between them.

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 ≤ 1,000 
  * 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 1,000 characters