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)

// lはlcmでよさそう（勘
// あとは順に埋めていって矛盾があれば終了 余ったところは適当に"a"入れればいいけど長さを答える問題なので必要ないね
package main

import "fmt"

func main() {
	var N, M int
	fmt.Scan(&N, &M)
	var S, T string
	fmt.Scan(&S, &T)
	SS, TT := make([]string, N), make([]string, M)
	for i, c := range []rune(S) {
		SS[i] = string(c)
	}
	for i, c := range []rune(T) {
		TT[i] = string(c)
	}
	L := lcm(N, M)
	X := make([]string, L)
	for i := 0; i < N; i++ {
		idx := i * L / N
		X[idx] = SS[i]
	}
	flag := true
	for i := 0; i < M; i++ {
		idx := i * L / M
		if X[idx] == "" {
			X[idx] = TT[i]
		} else if X[idx] == TT[i] {
			continue
		} else {
			flag = false
			break
		}
	}
	if flag {
		fmt.Println(L)
	} else {
		fmt.Println(-1)
	}
}

func lcm(a, b int) int {
	return (a * b) / gcd(a, b)
}

func gcd(a, b int) int {
	if a > b {
		a, b = b, a
	}
	for a > 0 {
		a, b = b%a, a
	}
	return b
}