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: Runtime Error)

import math
def main():
    n, m = list(map(int, input().split(" ")))
    s = input()
    t = input()

    if n < m:
        n, m = m, n
        s, t = t, s

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

    for i in range(lcm(n, m)+1):
        if i == 0:
            continue
        if i % n != 0 or i % m != 0:
            continue

        s_spliters = list(range(0, i, i // n))
        t_spliters = list(range(0, i, i // m))

        flag = True
        count = 0
        for t_spliter in t_spliters:
            if t_spliter in s_spliters:
                index = s_spliters.index(t_spliter)
                if s[index] != t[count]:
                    flag = False
                    break
            count += 1

        if flag:
            print(i)
            return
    print(-1)
if __name__ == "__main__":
    main()