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: Time Limit Exceeded)

def gcd(a, b):
  while b > 0:
    a, b = b, a%b
  return a

N,M = map(int,input().split(" "))
S = input()
T = input()
Answer = int(len(S)*len(T)/gcd(len(S),len(T)))
X = [0 for i in range(Answer)]

if (gcd(len(S),len(T)) == 1)and(S[0] == T[0]):
    print(Answer)
    exit()

for i in range(len(S)):
    X[int(i*Answer/len(S))] = S[i]

for i in range(len(T)):
    if (X[int(i*Answer/len(T))] == 0)or(X[int(i*Answer/len(T))] == T[i]):
        continue
    else:
        print(-1)
        exit()
print(Answer)