Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

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B. Nearest Fraction

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

Input

A single line contains three integers *x*, *y*, *n* (1 ≤ *x*, *y*, *n* ≤ 10^{5}).

Output

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

Examples

Input

3 7 6

Output

2/5

Input

7 2 4

Output

7/2

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