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: Accepted)

//ProblemA

//#define USE_STDIO
//#define USE_LOG
//#define FILE_ERR

#ifdef _MYPC
#include "mypc.h"
#endif // _MYPC

#ifndef debug
#define debug(...)
#endif // !LOG

#ifndef REDIRECT_STDIO
#define REDIRECT_STDIO {ios_base::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);}
#endif // REDIRECT_STDIO

//include
#include <iostream>
#include <string>
#include <vector>
#include <bitset>
#include <list>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <queue>
#include <stack>
#include <algorithm>
#include <numeric>
#include <functional>
#include <memory>
#include <complex>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <iomanip>

using namespace std;

//int
using ll = long long;
using ull = unsigned long long;
using uint = unsigned;

//pair
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;

//vector
template<typename T> using vt = std::vector<T>;
template<typename T> using vvt = vt<vt<T>>;
template<typename T> using vvvt = vt<vvt<T>>;
using vi = vt<int>;
using vvi = vvt<int>;
using vvvi = vvvt<int>;
using vl = vt<ll>;
using vvl = vvt<ll>;
using vvvl = vvvt<ll>;
using vb = vt<bool>;
using vpii = vt<pii>;

static inline ll Solve();

int main(int argc, char* argv[]) {
	REDIRECT_STDIO;

	cout << Solve() << endl;
	return 0;
}

ll gcd(ll x, ll y) {
	if(x % y == 0) return y;
	return gcd(y, x % y);
}

//ProblemA
ll Solve() {
	ll n, m;
	cin >> n >> m;
	string s, t;
	cin >> s >> t;

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

	ll i = 0, j = 0;
	while(i < n && j < m) {
		if(l / n * i == l / m * j) {
			if(s[i] != t[j]) return -1;
			i++, j++;
		} else if(l / n * i < l / m * j) {
			i++;
		} else {
			j++;
		}
	}
	return l;
}