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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

#sys.stdin.readline()
import sys
input = sys.stdin.readline

N,M = map(int,input().split())
S = list(input())
T = list(input())
judge = 1 #1:可,0:不可

def gcd(a,b):
 while(b>0):
    a,b = b,a%b
 return a
def lcm(a,b):
 G = gcd(a,b)
 L = (a*b)//G
 return L

L = lcm(N,M)
ans = L
#metrial = [] #[Xの何番目の要素に使われるか,要素]
p,q = L//N,L//M
for i in range(L):
  if((i%p == 0)and(i%q == 0)): 
    if(S[i//p] != T[i//q]):
      ans = -1
      break
print(ans)