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)

#include <bits/stdc++.h>

using namespace std;

#define inf 1<<30
#define llong long long
#define usd unsigned
#define pqueue priority_queue
#define mp make_pair
#define pb push_back
#define fn fill_n
typedef pair<int, int> P;
typedef struct data{
	int place;
	int cost;

	bool operator<(const data &ri) const{
		return cost < ri.cost;
	}
	bool operator>(const data &ri) const{
		return cost > ri.cost;
	}
}data;
int nw[9] = {0, 1, 0, -1, -1, 1, 1, -1, 0};
int nh[9] = {1, 0, -1, 0, 1, 1, -1, -1, 0};

llong int gcd(llong int a, llong int b){
	if(a < b) swap(a, b);
	while(b){
		a %= b;
		swap(a, b);
	}

	return a;
}

llong int lcm(llong int a, llong int b){
	return a / gcd(a, b) * b;
}
int main(){
	int q,w;
	string s, t;
	cin >> q >> w;
	cin >> s >> t;
	if(q<w){
		swap(s,t);
		swap(q,w);
	}
	llong int l = lcm(q,w);
	llong int g = gcd(q,w);
	llong int sg = q/g, tg = w/g;
	llong int si = 0, ti = 0;
	for(int i = 0; i < g; i++){
		// cout << si << s[si] << ti << t[ti] << endl;
		if(s[si] != t[ti]){
			cout << -1 << endl;
			return 0;
		}
		si += sg, ti += tg;
	}
	cout << l << endl;

	return 0;
}