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)

n,m=map(int,input().split())
s=input()
t=input()

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

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

if s[0]!=t[0]:
    print('-1')
    exit(0)

renl=lcm(n,m)
if renl!=n and renl!=m:
    print(renl)
    exit(0)
if n>=m:
    mx=s
    mn=t
else:
    mx=t
    mn=s
lmn=len(mn)
for i in range(lmn):
    if mx[i*renl//lmn]!=mn[i]:
        print('-1')
        exit(0)
print(renl)