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):
    if b == 0:
        return a
    return gcd(b, a % b)

def lcm(a, b):
    return (a * b) // gcd(a, b)

n, m = map(int, input().split())
s = input()
t = input()
if n == m and s == t:
    print(n)
elif max(n, m) % min(n, m) == 0:
    print(-1)
else:
    LCM = lcm(n, m)
    for i in range(1, m + 1):
        L = LCM * i
        x = ["" for i in range(L)]
        no = 0
        for i in range(n):
            x[i * L // n] = s[i]
        for i in range(m):
            if x[i * L // m] and x[i * L // m] != t[i]:
                no = 1
                break
            else:
                x[i * L // m] = t[i]
        if no:
            continue
        print(L)
        exit()