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)

import fractions as fr

N,M=[int(i) for i in input().split()]
S=input()
T=input()
Slist=list(S)
Tlist=list(T)
ans=0
GCD=0

if M==N:
    if S==T:
        ans=len(S)
    else:
        ans=-1
else:
    GCD=fr.gcd(N,M)
    if GCD==1:
        if Slist[0]==Tlist[0]:
            ans=int(N*M/GCD)
        else:
            ans=-1
    else:
        LCM=int(N*M/GCD)
        a=int(LCM/N)
        b=int(LCM/M)
        LCM2=int(a*b/fr.gcd(a,b))
        f=0
        for i in range(int(LCM/LCM2)):
            if Slist[i*b]!=Tlist[i*a]:
                f+=1
                break
        if f==0:
            ans=LCM
        else:
            ans=-1
print(ans)