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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main

import "fmt"

func Lcm(i, j int) int {
	temp := i * j
	for k := 2; k < temp; k++ {
		if k%i == 0 && k%j == 0 {
			return k
		}
	}
	return temp
}
func Min(i, j int) int {
	if i < j {
		return i
	}
	return j
}
func Gcd(i, j int) int {
	for k := Min(i, j); k >= 2; k-- {
		if i%k == 0 && j%k == 0 {
			return k
		}
	}
	return 1
}
func main() {
	var N, M int
	var S, T string
	fmt.Scan(&N, &M, &S, &T)

	L := Lcm(N, M)
	n := L / N
	m := L / M

	for i := 0; i < Gcd(N, M); i++ {
		if S[m*i] != T[n*i] {
			fmt.Println(-1)
			return
		}
	}
	fmt.Println(L)
}