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: Runtime Error)

#include <bits/stdc++.h>
// statics
using namespace std;
using int64 = int_fast64_t;
using PAIR = pair<int64, int64>;
constexpr int INF = 1 << 30;
constexpr int64 LINF = 1LL << 60;
constexpr int MOD = 1e9 + 7;
constexpr int MAX_N = 3e5 + 1;

// init/input
#define int int64
#define INIT ios::sync_with_stdio(false);cin.tie(0);
#define VAR(type, ...) type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T &t) {cin>>t;}
template<typename First, typename...Rest> void MACRO_VAR_Scan(First &first, Rest&...rest) {cin>>first;MACRO_VAR_Scan(rest...);}
#define VEC(type, c, n) vector<type> c(n);for(auto &&i:c)cin>>i;

// out
#define OUT(dist) cout<<(dist);
#define FOUT(n, dist) cout<<fixed<<setprecision(n)<<(dist);
#define SP cout<<" ";
#define BR cout<<endl;
#define zero(n) cout<<setfill('0')<<right<<setw(n)
#define debug(x) cerr<<#x<<":"<< (x);BR;

// utility
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define EACH(i, a) for(auto &&i:(a))
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define RFOR(i, a, b) for(int i=(b)-1;i>=(a);--i)
#define REP(i, n) for(int i=0;i<(n);++i)
#define RREP(i, n) for(int i=(n)-1;i>=0;--i)
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
int gcd(int a,int b){
	return (a%b==0?b:gcd(b,a%b));
}

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

signed main() {
  INIT;
	VAR(int,n,m);
	VAR(string,s,t);
  int len = n*m/gcd(n,m);

	vector<char> str(1e8,'?');
	bool ok = true;
	REP(ni,n){
		str[ni*len/n] = s[ni];
	}
	REP(mi,m){
		if(str[mi*len/m]!='?') ok &= str[mi*len/m] == t[mi];
		str[mi*len/m] = t[mi];
	}
	OUT(ok?len:-1)BR;
  return 0;
}