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: Wrong Answer)

<?php
function gcd($a, $b) {
	if ($b === 0)
		return $a;

	return gcd($b, $a % $b);
}

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

$NM = explode(" ", trim(fgets(STDIN)));
$N = $NM[0];
$M = $NM[1];
$S = trim(fgets(STDIN));
$T = trim(fgets(STDIN));
$L = -1;
$SNumber;
$TNumber;

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

for($i = 0; $i < $N; $i++)
	$SNumber[] = $i * $L / $N;

for($i = 0; $i < $M; $i++)
	$TNumber[] = $i * $L / $M;

for($i = 0; $i < count($SNumber); $i++){
	if($SNumber[$i] >= $N)
		break;
	if(array_search($SNumber[$i], $TNumber) != false){
		if(strcmp(substr($S, $SNumber[$i], 1), substr($T, $TNumber[array_search($SNumber[$i], $TNumber)], 1)) != 0){
			$L = -1;
			break;
		}
	}
}
printf("%d", $L);
?>