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 Python (3.4.3) (judge verdict: Accepted)

import fractions


def lcm(x, y):
    return x // fractions.gcd(x, y) * y


def solve(n, m, s, t):
    le = lcm(n, m)
    s_new_ps = {le // n * i for i in range(n)}
    t_new_ps = {le // m * i for i in range(m)}
    conf_new_ps = s_new_ps & t_new_ps
    for p in conf_new_ps:
        i = p // (le // n)
        j = p // (le // m)
        if s[i] != t[j]:
            return None
    return le


def main():
    n, m = (int(z) for z in input().split())
    s = input()
    t = input()
    res = solve(n, m, s, t)
    if res is None:
        print(-1)
    else:
        print(res)


if __name__ == '__main__':
    main()