CF222C.Reducing Fractions

To confuse the opponents, the Galactic Empire represents fractions in an unusual format. The fractions are represented as two sets of integers. The product of numbers from the first set gives the fraction numerator, the product of numbers from the second set gives the fraction denominator. However, it turned out that the programs that work with fractions in this representations aren't complete, they lack supporting the operation of reducing fractions. Implement this operation and the Empire won't forget you.

为了迷惑对手，银河帝国以一种不寻常的格式表示分数。分数由两组整数表示：第一组整数的乘积作为分数的分子，第二组整数的乘积作为分数的分母。然而，人们发现，处理这种表示形式分数的程序并不完善——它们缺少约分操作的支持。请实现这一约分操作，银河帝国将不会忘记你。

The first input line contains two space-separated integers n, m (1 ≤ n, m ≤ 105) that show how many numbers the first set (the numerator) and the second set (the denominator) contain, correspondingly.

The second line contains n space-separated integers: _a_1, _a_2, ..., a__n (1 ≤ a__i ≤ 107) — the numbers that are multiplied to produce the numerator.

The third line contains m space-separated integers: _b_1, _b_2, ..., b__m (1 ≤ b__i ≤ 107) — the numbers that are multiplied to produce the denominator.

第一行输入包含两个用空格分隔的整数 $n$、$m$（$1 ≤ n, m ≤ 10^5$），分别表示第一个集合（分子）和第二个集合（分母）中数字的个数。

第二行包含 $n$ 个用空格分隔的整数：$a_1,\,a_2,\,...,\,a_n$（$1 ≤ a_i ≤ 10^7$）——这些数字相乘得到分子。

第三行包含 $m$ 个用空格分隔的整数：$b_1,\,b_2,\,...,\,b_m$（$1 ≤ b_i ≤ 10^7$）——这些数字相乘得到分母。

Print the answer to the problem in the form, similar to the form of the input data. The number of values in the sets you print n__out, m__out must satisfy the inequality 1 ≤ n__out, m__out ≤ 105, and the actual values in the sets a__out, i and b__out, i must satisfy the inequality 1 ≤ a__out, i, b__out, i ≤ 107.

Separate the values in the lines by spaces. The printed fraction must be reduced, that is, there mustn't be such integer x (x > 1), that the numerator and the denominator of the printed fraction are divisible by x. If there are several matching answers, print any of them.

以与输入数据相同的形式输出问题的答案。您所输出的集合中的元素个数 $n_{\text{out}}$、$m_{\text{out}}$ 必须满足不等式 $1 \leq n_{\text{out}},\, m_{\text{out}} \leq 10^5$，且集合中实际的元素值 $a_{\text{out},i}$ 和 $b_{\text{out},i}$ 必须满足不等式 $1 \leq a_{\text{out},i},\, b_{\text{out},i} \leq 10^7$。

每行内的数值用空格分隔。所输出的分数必须为最简形式，即不存在整数 $x$（$x > 1$），使得该分数的分子与分母均能被 $x$ 整除。若存在多个符合条件的答案，输出任意一个即可。

In the first test sample the numerator equals 1000, the denominator equals 500. If we reduce fraction 1000/500 by the greatest common divisor of the numerator and the denominator (by 500), we obtain fraction 2/1.

In the second test sample the numerator equals 2000, the denominator equals 300. If we reduce fraction 2000/300 by the greatest common divisor of the numerator and the denominator (by 100), we obtain fraction 20/3.

在第一个测试样例中，分子为 1000，分母为 500。若用分子与分母的最大公约数（即 500）约简分数 $\frac{1000}{500}$，可得最简分数 $\frac{2}{1}$。

在第二个测试样例中，分子为 2000，分母为 300。若用分子与分母的最大公约数（即 100）约简分数 $\frac{2000}{300}$，可得最简分数 $\frac{20}{3}$。