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 PHP (5.6.30) (judge verdict: Accepted)

<?php
//error_reporting(0);
//$N = trim(fgets(STDIN));
list($N,$M) = explode(" ",trim(fgets(STDIN)));
//$v = explode(" ",trim(fgets(STDIN)));
$S = trim(fgets(STDIN));
$T = trim(fgets(STDIN));

$L = lcm($N,$M);

for($i=1;$i<5;$i++) {
  $sz = $i*$L;
  $a = array();

  $ng = 0;
  for($j=0;$j<=$N-1;$j++) {
    $p = (int)($j*($sz/$N))+1;
    if (isset($a[$p-1])&&$a[$p-1]!=$S[$j]) {
      $ng = 1;
      break;
    }
    $a[$p-1]=$S[$j];
  }
  for($j=0;$j<=$M-1;$j++) {
    $p = (int)($j*($sz/$M))+1;
    if (isset($a[$p-1])&&$a[$p-1]!=$T[$j]) {
      $ng = 1;
      break;
    }
    $a[$p-1]=$T[$j];
  }
  if ($ng == 0) {
    printf("%d\n",$i*$L);
    exit;
  }
}
printf("-1\n");

function gcd($a,$b) {
    if ($b == 0) return $a;
      return gcd($b,$a%$b);
}
function lcm($a,$b) {
    $l = gcd($a,$b);
      return $a / $l * $b;
}