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 (7.3.0) (judge verdict: Time Limit Exceeded)

import fractions
def lcm(x, y):
    return (x * y) // fractions.gcd(x, y)
n,m=map(int,input().split())
s=input()
t=input()
if s[0]!=t[0]:
    print(-1)
    exit()
k=lcm(n,m)
ans=[""for i in range(k)]
ans[0]=s[0]
for i in range(1,n):
    ans[i*(k//n)]=s[i]
for i in range(1,m):
    if not ans[i*(k//m)]:
        ans[i*(k//m)]=t[i]
    else:
        if ans[i*(k//m)]!=t[i]:
            print(-1)
            exit()
print(k)