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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define fin(ans) cout << (ans) << endl;
#define blank(ans) cout << (ans) << " ";
#define mp(p, q) make_pair(p, q)
#define mt(p, q, r) make_tuple(p, q, r)
#define pb(n) push_back(n)
#define all(a) a.begin(), a.end()

typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef string str;

typedef vector<ll> vll;
typedef vector<ld> vd;
typedef vector<bool> vb;
typedef vector<char> vc;
typedef vector<str> vs;
typedef vector<vector<ll>> vvll;
typedef vector<vector<ld>> vvd;
typedef vector<vector<char>> vvc;
typedef vector<vector<str>> vvs;
typedef vector<pair<ll, ll>> vpll;
typedef vector<tuple<ll, ll, ll>> vtlll;

const ld PI = acos(-1.0);
const ll MAX = 9000000000000000000;
const ll MIN = -9000000000000000000;
const ld DMAX = 4500;
const ld DMIN = -4500;
const ll MOD = 1000000007;

ll gcd(ll a, ll b)
{
  return b ? gcd(b, a % b) : a;
}

ll lcm(ll a, ll b)
{
  return a * b / gcd(a, b);
}

//実行部
void Main()
{
  ll n, m; cin >> n >> m;
  str s, t; cin >> s >> t;
  if(n % m == 0||m % n == 0) fin(-1)
  else fin(lcm(n, m))
}

//前処理
int main()
{
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(20); //高精度少数表示
  Main();
  return 0;
}