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 (3.8.2) (judge verdict: Runtime Error)

from math  import gcd
n, m = map(int, input().split())
s = input()
t = input()

ans = n*m//gcd(n, m)

if n==1:
    if t == s*m:
        print(m)
    else:
        print(-1)
    exit(0)
elif m == 1:
    if s == t**n:
        print(n)
    else:
        print(-1)
    exit(0)

"""
最小公倍数の長さで収まらない場合は、何をやってもダメ
"""
dp = [0] * ans
for i in range(n):
    dp[i*ans//n] = s[i]

for i in range(m):
    if dp[i*ans//m] == 0: 
        dp[i*ans//m] = t[i]
    else:
        if dp[i*ans//m] != t[i]:
            print(-1)
            exit(0)
print(ans)