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 {
	for k := 2; ; k++ {
		if k%i == 0 && k%j == 0 {
			return k
		}
	}
}
func main() {
	var n, m int
	var s, t string
	fmt.Scan(&n, &m, &s, &t)

	lcm := Lcm(n, m)
	count := 1
	if s[0] != t[0] {
		fmt.Println(-1)
		return
	}
	for {
		L := lcm * count
		num1 := L / n
		num2 := L / m
		lcm2 := Lcm(num1, num2)

		for i := 1; i*lcm2+1 <= L; i++ {
			if s[(i*lcm2-1)/num1+1] == t[(i*lcm2-1)/num2+1] {
				if i == (L-1)/lcm2 {
					fmt.Println(L)
					return
				}
				continue
			} else {
				fmt.Println(-1)
				return
			}
		}
		count++
	}
}