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()

cnt = 1
ns = 1
nt = 1
ss = 0
tt = 0
fail = False

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

ll = (n * m) // gcd(n, m)
l = ll

while l <= n * m:
    fail = False
    while not( ns >= l or nt >= l):
        while not(ns <= nt):
            nt += l / m 
            tt += 1

        if(ns == nt) and (s[ss] != t[tt]):
            fail = True
            break

        ns += l / n
        ss += 1
    if not(fail): 
        break
    cnt += 1
    l = ll * cnt

if(fail):
    print(-1)
else:
    print(l)