Problem3535--Nearest Fraction

3535: Nearest Fraction

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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).

Examples
Input
3 7 6
Output
2/5
Input
7 2 4
Output
7/2

Source/Category

 
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