# Farey sequences

# Farey sequences

A fraction **h** / **k** is called a proper fraction if it lies between **0** and **1** and if **h** and **k** have no common factors. For any positive integer **n** ≥ **1**, the Farey sequence of order **n**, `F`

, is the sequence of all proper fractions with denominators which do not exceed _{n}**n** together with the "fraction" **1** / **1**, arranged in increasing order. So, for example, `F`

is the sequence:_{5}

For a given **n**, you are to find the **k**-th fraction in the sequence `F`

._{n}

#### Input

Input consists of a sequence of lines containing two natural numbers **n** and **k**, **1** ≤ **n** ≤ **1000** and **k** sufficiently small such that there is the **k**-th term in `F`

. (The length of _{n}`F`

is approximately _{n}**0.3039635n^2**).

#### Output

For each line of input print one line giving the **k**-th element of `F`

in the format as shown in example._{n}

5 5 5 1 5 9 5 10 117 348 288 10000

1/2 1/5 4/5 1/1 9/109 78/197