Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Reducing Fractions

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputTo 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.

Input

The first input line contains two space-separated integers *n*, *m* (1 ≤ *n*, *m* ≤ 10^{5}) 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} ≤ 10^{7}) — 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} ≤ 10^{7}) — the numbers that are multiplied to produce the denominator.

Output

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} ≤ 10^{5}, 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} ≤ 10^{7}.

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.

Examples

Input

3 2

100 5 2

50 10

Output

2 3

2 1

1 1 1

Input

4 3

2 5 10 20

100 1 3

Output

1 1

20

3

Note

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.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Dec/11/2017 10:38:49 (c5).

Desktop version, switch to mobile version.

User lists

Name |
---|