#P281B. Nearest Fraction

    ID: 5823 远端评测题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 5 上传者: 标签>brute forceimplementationtwo pointers*1700

Nearest Fraction

Description

You are given three positive integers x, y, n. Your task is to find the nearest fraction to fraction whose denominator is no more than n.

Formally, you should find such pair of integers a, b (1 ≤ b ≤ n; 0 ≤ a) that the value is as minimal as possible.

If there are multiple "nearest" fractions, choose the one with the minimum denominator. If there are multiple "nearest" fractions with the minimum denominator, choose the one with the minimum numerator.

A single line contains three integers x, y, n (1 ≤ x, y, n ≤ 105).

Print the required fraction in the format "a/b" (without quotes).

Input

A single line contains three integers x, y, n (1 ≤ x, y, n ≤ 105).

Output

Print the required fraction in the format "a/b" (without quotes).

Samples

3 7 6

2/5

7 2 4

7/2