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。