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 PyPy3 (2.4.0) (judge verdict: Runtime Error)

import fractions
N,M=map(int,input().split())
S=input()
T=input()
lcm=(N*M)/fractions.gcd(N,M)
num=0
s=[]
t=[]
flag=1
for i in range(max(N,M)):
    num=lcm*(i+1)
    st=[""]*int(num)
    for j in range(N):
        if st[int(1+(num//N)*j)-1]=="":
            st[int(1 + (num // N) * j)-1]=S[j]
        elif st[int(1+(num//N)*j)-1]!=S[j]:
            flag=0
            break
    for j in range(M):
        if st[int(1+(num//M)*j)-1]=="":
            st[int(1 + (num // M) * j)-1]=T[j]
        elif st[int(1+(num//M)*j)-1]!=T[j]:
            flag=0
            break
    if flag==1:
        break
    #print(s,t)
    s=[]
    t=[]
if flag==0:
    print("-1")
else:
    print(len(st))