# Problem G

Farey Sums

Given a positive integer, $N$, the sequence of all fractions
$a / b$ with $0 \le a \le b$, $1 \le b \le N$, and $a$ and $b$ relatively prime, listed in
increasing order, is called the *Farey Sequence of order
$N$*.

For example, the *Farey Sequence of order $6$* is:

If the denominators of the *Farey Sequence of order
$N$* are:

then the *Farey Sum of order $N$* is the sum of $b_ i / b_{i+1}$ from $i = 1 \ldots K-1$.

For example, the *Farey Sum of order $6$* is:

Write a program to compute the *Farey Sum of order
$N$* for a given
$N$.

## Input

The first line of input contains a single integer $P$ ($1 \le P \le 9\, 999$), which is the number of data sets that follow. Each data set should be processed identically and independently.

Each data set consists of a single line of input. It
contains the data set number, $K$, followed by the order
$N$ ($2 \le N \le 10\, 000$) of the
*Farey Sum* that is to be computed.

## Output

For each data set there is a single line of output. The
single output line consists of the data set number,
$K$, followed by a single
space followed by the *Farey Sum* as a decimal fraction
in lowest terms. If the denominator is $1$, print only the numerator.

Sample Input 1 | Sample Output 1 |
---|---|

4 1 6 2 15 3 57 4 9999 |
1 35/2 2 215/2 3 2999/2 4 91180457/2 |