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)

N, M = list(map(int, input().split()))
S = input()
T = input()

from fractions import gcd
L = (N * M) // gcd(N, M)

L1 = [1]
L2 = [1]
for i in range(1, N):
    t = i * (L // N) + 1
    L1.append(t)

for i in range(1, M):
    t = i * (L // M) + 1
    L2.append(t)

LS = [None] * L
for i, li in enumerate(L1):
    ind = li-1
    LS[ind] = S[i]

ans = True
for i, li in enumerate(L2):
    ind = li-1
    if LS[ind] is not None:
        if LS[ind] != T[i]:
            ans = False

if ans:
    print(L)
else:
    print(-1)


# print(L1)
# print(L2)
# print(LS)