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);

//最大公約数
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;
}
 
//最小公倍数
function lcm($m, $n){
    return $m * $n / gcd($m, $n);
}

$lcmnm = lcm($n, $m);

$l = [];

for ($i = 0; $i < $n; $i++) {
    $l[$lcmnm / $n * $i] = $s[$i];
}

$result = true;
for ($i = 0; $i < $m; $i++) {
    if (isset($l[$lcmnm / $m * $i]) && $l[$lcmnm / $m * $i] != $t[$i]) {
        $result = false;
        break;
    }
}

if ($result) {
    echo $lcmnm . "\n";
} else {
    echo "-1\n";
}