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)

import math
def lcm(x, y):
    return (x * y) // math.gcd(x, y)

N,M = map(int,input().split())
S = str(input())
T = str(input())

L = lcm(N,M)
if L == max(N,M):
  L *= 2
X = [""]*L
if S[0] != T[0]:
  print(-1)
  exit()
else:
  X[0] = S[0]

for i in range(1,N):
  X[i*L//N] = S[i]
for j in range(1,M):
  if X[j*L//M] == "":
    X[j*L//M] = T[j]
  elif X[j*L//M] == T[j]:
    pass
  else:
    print(-1)
    exit()

print(L)