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
fscanf(STDIN, "%d %d", $N, $M);
fscanf(STDIN, "%s", $S);
fscanf(STDIN, "%s", $T);
$ans = lcm($N, $M);

$step = $ans / $N;
for ($i = 0; $i < $N; $i++) {
    $SS[$i * $step] = $S[$i];
}

$step = $ans / $M;
for ($i = 0; $i < $M; $i++) {
    $TT[$i * $step] = $T[$i];
}

$bool = true;
foreach ($SS as $k => $v) {
    if (isset($TT[$k]) && $SS[$k] !== $TT[$k]) {
        $bool = false;
    }
}

echo $bool ? $ans : '-1';

function gcd($m, $n){
    if($n > $m) list($m, $n) = array($n, $m);
     
    while($n !== 0){
        $tmp_n = $n;
        $n = $m % $n;
        $m = $tmp_n;
    }
    return $m;
}
 
function lcm($m, $n){
    return $m * $n / gcd($m, $n);
}