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: Accepted)

import fractions
n, m = map(int,input().split())
s = list(map(str,input()))
t = list(map(str,input()))
k = 0
q = fractions.gcd(n, m)
l = n * m // q #lcm(n, m)
p = int(l/n * l/m / fractions.gcd(l/n, l/m)) #lcm(l/n, l/m)
for i in range(0, int(l/p)):
  if s[0] != t[0]:
    print('-1')
    break
  elif q == 1:
    print(l)
    break
  elif s[i * p//(l//n)] != t[i * p//(l//m)]:
    print('-1')
    break
  else:
    k = k + 1

if k == l/p:
  print(l)