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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

//Ruthless Coding 
#include <bits/stdc++.h>

#define uni(x)      (x).resize(unique(ALL(x)) - (x).begin())
#define fprint(v)   for(auto x : v) cout << x << ' '
#define ALL(x)      (x).begin(), (x).end()
#define MP(x, y)    make_pair(x, y)
#define SZ(x)       int((x).size())
#define PB(x)       push_back(x)
#define ll          long long
#define S           second 
#define F           first
#define nl          '\n'

using namespace std;
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}

template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifndef ONLINE_JUDGE
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif
mt19937_64 rnd;

const int N = 2e5 + 5;
ll gc(ll a, ll b){
    if(b == 0) return a;
    return gc(b, a % b);
}
int lcm(ll a, ll b){
    return int((a * b) / gc(a, b));
}
string s, t;
bool check(int len){
    int n = s.size();
    int m = t.size();
    map<int, char> mp;
    for(int i = 0; i < n; i++){
        int idx = i * (len / n) + 1;
        mp[idx] = s.at(i);
    }
    for(int i = 0; i < m; i++){
        int idx = i * (len / m) + 1;
        if(!mp.count(idx)){
            mp[idx] = t.at(i);
        }else{
            if(mp[idx] != t[i]){
                return false;
            }
        }
    }
    return true;
}
int main() {
    ios_base::sync_with_stdio(0);cin.tie(0);
    int n, m;
    cin >> n >> m;
    cin >> s >> t;
    int d = lcm(n, m);
    int lo = 0, hi = 1e5;
    while(hi - lo > 1){
        int mid = lo + hi >> 1;
        if(check(mid * d)) hi = mid;
        else lo = mid;
    }
    if(hi == 1e5){
        cout << -1;
    }else{
        cout << hi * d;
    }
    return 0;
}
/*
    *** Most Impo.. -> check base case always
    1. Overflow Check (*, +)
    2. Index check (0 - based or 1 - based)
    3. Check for n = 1, 2, 3, 4....
    4. Corner Cases
*/