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 fractions


def main():
    N, M = map(int, input().split())
    S = input()
    T = input()
    L = int((N*M) / fractions.gcd(N, M))
    X_S = S_ni_naru([0]*L, S, L, N)
    X_T = T_ni_naru([0]*L, T, L, M)

    for s, t in zip(X_S, X_T):
        if (s != t) and (s != 0) and (t != 0):
            print(-1)
            exit()

    print(L)


def S_ni_naru(X_S, S, L, N):
    s_i = 0
    for i in range(N):
        if i == 0:
            idx = 0
        else:
            idx = int((L*i)/N)

        X_S[idx] = S[s_i]
        s_i = s_i + 1

    return X_S


def T_ni_naru(X_T, T, L, M):
    t_i = 0
    for i in range(M):
        if i == 0:
            idx = 0
        else:
            idx = int((L*i)/M)

        X_T[idx] = T[t_i]
        t_i = t_i + 1

    return X_T


if __name__ == "__main__":
    main()