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: Runtime Error)

import fractions
N,M = map(int,input().split())
S = input()
T = input()
X = (N * M) // fractions.gcd(N,M)

div_N = X // N
div_M = X // M  
s = [""] * X

for ss in range(N):
  if ss == 0:
    s[0] = S[0]
    if s[0] != T[0]:
      print(-1)
      exit()
  else:
    s[ss * (div_N)] = S[ss]

for tt in range(M):
  if tt == 0:
    if s[0] != T[tt]:
      print(-1)
      exit()
  else:
    pro = tt * (div_M)
    if s[pro] != "" and s[pro] != T[tt]:
      print(-1)
      exit()
print(X)