## Description:

In sixth grade, students are presented with different ways to calculate the *Least Common Multiple*(**LCM**) and the *Greatest Common Factor *(**GCF**) of two integers. The **LCM **of two integers *a *and *b *isthe smallest positive integer that is a multiple of both *a *and *b*. The **GCF **of two non-zero integers *a*and *b *is the largest positive integer that divides both *a *and *b *without remainder.For this problem you will write a program that determines both the **LCM **and **GCF **for positiveintegers.

## Input:

The first line of input contains a single integer *N*, (1 ￡ *N *￡ 1000) which is the number of data sets thatfollow. Each data set consists of a single line of input containing two positive integers, *a *and *b*,(1 ￡ *a,b *￡ 1000) separated by a space.

## Output:

For each data set, you should generate one line of output with the following values: The data setnumber as a decimal integer (start counting at one), a space, the **LCM**, a space, and the **GCF**.

## Sample Input:

3

5 10

7 23

42 56

## Sample Output:

1 10 5

2 161 1

3 168 14

## Note:

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本题由旧版NOJ导入，来源：ACM ICPC Greater New York Region 2008