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: Accepted)

N,M = list(map(int,input().split()))
S = input()
T = input()
sl = list(S)
tl = list(T)
def gcd(a, b):
	while b:
		a, b = b, a % b
	return a
def lcm(x, y):
    return int((x * y) / gcd(x, y))

lcm = lcm(N,M)
Sd = int(lcm/N)
St = int(lcm/M)
kaisu = min(int((N-1)/St),int((M-1)/Sd))
flag = 0
for i in range(kaisu+1):
    if sl[St*i] != tl[Sd*i]:
        flag = 1
if flag == 0:
    print(lcm)
else:
    print(-1)