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: Wrong Answer)

import fractions
N,M = map(int,input().split())
S = input()
T = input()
if N>=M:
  if N%M!=0:
    x = fractions.gcd(N,M)
    if S[0]==T[0]:
      print (int(N*M/x))
    else:
      print (-1)
  else:
    x = int(N/M)
    a = []
    b = []
    for i in range(M):
      a.append(S[i*x])
    for i in range(M):
      b.append(T[i])
    if a==b:
      print (N)
    else:
      print (-1)
else:
  if M%N!=0:
    if S[0]==T[0]:
      x = fractions.gcd(N,M)
      print (int(M*N/x))
    else:
      print (-1)
  else:
    x = int(M/N)
    a = []
    b = []
    for i in range(N):
      a.append(T[i*x])
    for i in range(N):
      b.append(S[i])
    if a==b:
      print (M)
    else:
      print (-1)