# 2723. Sixth Grade Math

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 is the 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 positive integers.

### 输入格式

The first line of input contains a single integer N, (1 <= N <= 1000) which is the number of data sets that follow. 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.

### 输出格式

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

### 样例

Input
3
5 10
7 23
42 56

Output
1 10 5
2 161 1
3 168 14


162 人解决，169 人已尝试。

182 份提交通过，共有 267 份提交。

1.5 EMB 奖励。