Problem:
Score : 300 points

Problem Statement

You are given a string S of length N and another string T of length M.
These strings consist of lowercase English letters.

A string X is called a good string when the following conditions are all met:

Let L be the length of X. L is divisible by both N and M.

Concatenating the 1-st, (\frac{L}{N}+1)-th, (2 \times \frac{L}{N}+1)-th, ..., ((N-1)\times\frac{L}{N}+1)-th characters of X, without changing the order, results in S.

Concatenating the 1-st, (\frac{L}{M}+1)-th, (2 \times \frac{L}{M}+1)-th, ..., ((M-1)\times\frac{L}{M}+1)-th characters of X, without changing the order, results in T.

Determine if there exists a good string. If it exists, find the length of the shortest such string.

Constraints

1 \leq N,M \leq 10^5

S and T consist of lowercase English letters.

|S|=N

|T|=M

Input

Input is given from Standard Input in the following format:

N M
S
T

Output

If a good string does not exist, print -1; if it exists, print the length of the shortest such string.

Sample Input 1

3 2
acp
ae

Sample Output 1

6

For example, the string accept is a good string.
There is no good string shorter than this, so the answer is 6.

Sample Input 2

6 3
abcdef
abc

Sample Output 2

-1

Sample Input 3

15 9
dnsusrayukuaiia
dujrunuma

Sample Output 3

45

Solution in PHP7 (7.0.15) (judge verdict: Accepted)

<?php
list($n, $m) = explode(" ", trim(fgets(STDIN)));
$N = trim(fgets(STDIN));
$M = trim(fgets(STDIN));

$gcd = gcd($n, $m);
$len = lcm($n, $m);

for($i = 0; $i < $n; $i++){
    $c[$i * $m / $gcd] = $N[$i];
}
$flag = true;
for($i = 0; $i < $m; $i++){
    if(isset($c[$i * $n / $gcd]) && $M[$i] != $c[$i * $n / $gcd])$flag = false;
    $c[$i * $n / $gcd] = $M[$i];
}
if($flag){
    echo $len;
}else{
    echo -1;
}

function gcd($m, $n){
    if(!$n)return $m;
    return gcd($n, $m % $n);
}

function lcm($a, $b) {
    return $a * $b / gcd($a, $b);
}