UTS Programming Competition 2014 Problem 4

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Problem 4: Greatest Common Divisor

Run time limit: 10 seconds

Problem Description

The greatest common divisor, or GCD, of two or more integers is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 8 and 12 is 4.

Your task is to find, in a list of integers, the two largest numbers that yield the largest GCD.

Data Specification

Input

Multiple lines of input with multiple integers on each line, separated by spaces. Each number shall greater than 1 and less than 1,000,000. There shall be up to 100 numbers on each line. Each line shall be terminated with a zero (0).

The final line of input shall be marked with a solitary zero (0).

Output

For each line of input, output the two largest numbers that yield the largest GCD, and their GCD.

Sample Input

4 8 24 0 
7 11 2 13 23 0 
48 64 24 72 0 
0 

Sample Output

8 24 8
13 23 1
48 72 24

Solutions

Put your solutions here!

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