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[n], is the sequence of all proper fractions with denominators which do not exceed n together with the "fraction" 1 / 1, arranged in increasing order. So, for example,
F is the sequence:
For a given n, you are to find the k-th fraction in the sequence
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[n]. (The length of
F[n] is approximately 0.3039635n^2).
For each line of input print one line giving the k-th element of
F[n] in the format as shown in example.
5 5 5 1 5 9 5 10 117 348 288 10000
1/2 1/5 4/5 1/1 9/109 78/197