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 = list(input())
t = list(input())

l = n*m//fractions.gcd(n,m)

c = ['']*l
d = ['']*l

c[0] = s[0]
a = [0]
for i in range(1,n):
    c[i*(l//n)] = s[i]
    a.append(i*(l//n))

d[0] = t[0]
b = [0]
for i in range(1,m):
    d[i*(l//m)] = t[i]
    b.append(i*(l//m))

ans = l

e = set(a)&set(b)

for i in e:
    if c[i] == d[i]:
        1
    else:
        ans = -1
        break

if l ==n or l ==m:
    ans = -1
       
print(ans)