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<stdio.h>
#include<iostream>
#include<algorithm>
#include<string>
#include<string.h>
#include<math.h>
#include<stdlib.h>
#include<vector>
#include<queue>
#include<map>
#include<tuple>
#define rep(index,num) for(int index=0;index<num;index++)
#define rep1(index,num) for(int index=1;index<=num;index++)
#define scan(argument) cin>>argument
#define prin(argument) cout<<argument<<endl
#define kaigyo cout<<endl
#define eps 1e-15
#define mp(a1,a2) make_pair(a1,a2)
typedef long long ll;
using namespace std;
typedef pair<ll,ll> pll;
typedef pair<int,int> pint;
typedef vector<int> vint;
typedef vector<ll> vll;
typedef vector<pint> vpint;
typedef vector<pll> vpll;
ll INFl=1e+18+1;
int INF=1e+9+1;
ll gcd(ll x,ll y){
	if(y==0) return x;
	return gcd(y,x%y);
}
ll lcm(ll x,ll y){
	return x/gcd(x,y)*y;
}
int main(){
	ll N,M;
	string S,T;
	scan(N);scan(M);
	scan(S);scan(T);
	ll L=lcm(N,M);
	ll soki=L/M,toki=L/N;
	ll num=L/soki;
	int flag=1;
	vector<char> stest,ttest;
	rep(i,N){
		if(i%soki==0) stest.push_back(S[i]);
	}
	rep(i,M){
		if(i%toki==0) ttest.push_back(T[i]);
	}
	/*rep(i,stest.size()){
		printf("%c",stest[i]);
	}
	kaigyo;
	rep(i,ttest.size()){
		printf("%c",ttest[i]);
	}
	kaigyo;*/
	if(stest==ttest) prin(L);
	else prin(-1);
	return 0;
}