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)

# coding:utf-8
import sys
import os
import math

n, m = map(int, input().split())
s = input()
t = input()
ans_str = ""
count_n = 1
count_m = 1

l = (n * m) // math.gcd (n, m)
ans_str_list = [""]*l 

if(s[0] == t[0]):
    ans_str_list[0] = s[0]
for i in range(l-1):
    #print("i+1 is : {}".format(i+1))
    #print("count_n*(l/n)+1 is : {}".format(count_n*(l/n)+1))
    if i+1 == count_n*(l/n)+1:
        ans_str_list[i+1] = s[count_n]
        count_n += 1
    if i+1 == count_m*(l/m)+1:
        ans_str_list[i+1] = t[count_m]
        count_m += 1
        #print("m done")
        
for j in range(l):
    if ans_str_list[j] == "":
        ans_str_list[j] = " "
    ans_str += ans_str_list[j]
ans = len(ans_str_list)

count_n = 1
count_m = 1
for k in range(l-1):
    if(k+1 <= len(s)):
        if k+1 == count_n*(l/n)+1:
            if(ans_str[k+1] != s[count_n]):
                ans = -1
                break
            count_n += 1
    if(k+1 <= len(t)):
        if k+1 == count_m*(l/m)+1:
            if(ans_str[k+1] != t[count_m]):
                #print("check m")
                ans = -1
                break
            count_m += 1
print("{}".format(ans))