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: Runtime Error)

#
# N M
# S
# T
#
# find X (length L, LはN, Mで割り切れる (最小公倍数))
#
# e.g.
# 3 2
# acp
# ae
#
# X
# - 
# - 1, L/N+1, 2L/N+1, ... はSになる
# - 1, L/M+1, 2L/M+1, ... はTになる

from fractions import gcd

N, M = map(int, input().split())
S = input()
T = input()
L = N * M // gcd(N, M)

if S[0] != T[0]:
    print(-1)
    exit()

# 仮の文字列 (中身は何でもいい)
ans = [S[0]] + ["-"] * (L - 1)

# Sを置く
for i in range(N):
    ans[i * L // N] = S[i]

# print(ans)

# Tを置く
# 既にSが入っている場合，Tと整合するか確認する
for i in range(M):
    index = i * L // M
    if ans[index] != "-":
        if ans[index] != T[i]:
            print(-1)
            exit()
        else:
            ans[index] = T[i]
    else:
        ans[index] = T[i]


print(L)