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)

inp = input()
NM,S,T = [input() for i in range(inp)]


listed_NM = list(map(int, NM.split()))
N = listed_NM[0]
M = listed_NM[1]
listed_S = list(S)
listed_T = list(T)
lcm = int(N*M/math.gcd(N,M))

list_S = [i*lcm/N+1 for i in range(N)]
list_T = [i*lcm/M+1 for i in range(M)]

set_S = {i*lcm/N+1 for i in range(N)}
set_T = {i*lcm/M+1 for i in range(M)}


inter = set_S.intersection(set_T)
for j,i in enumerate(inter):
    index_S = list_S.index(i)
    index_T = list_T.index(i)
    if listed_S[index_S] != listed_T[index_T]:
        print(-1)
        break
    elif j+1==len(inter):
    #else:
        print(lcm)