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: Wrong Answer)

#include<cstdio>
int gcd_euclid(int u, int v) {
  int r;
  while (0 != v) {
    r = u % v; u = v; v = r; /* swap */
  }
  return u;
}
int main(){
	int N, M;
	scanf("%d %d\n", &N, &M);
	char S[N + 1], T[M + 1];
	scanf("%s", S);
	scanf("%s", T);
	if(S[0] != T[0]){
		printf("-1\n");
		return 0;
	}
	int gcd = gcd_euclid(N, M);
	long long answer = (long long)N/gcd*M;
	if(N % M && M % N){
		printf("%lld\n", answer);
		return 0;
	}
	if(N >= M){
		for (int i = 1; i < M; ++i){
			if(S[N/M*i] != T[i]){
				printf("-1\n");
				return 0;
			}
		}
		printf("%lld\n", answer);
		return 0;
	}
	for (int i = 1; i < N; ++i){
		if(S[i] != T[M/N*i]){
			printf("-1\n");
			return 0;
		}
	}
	printf("%lld\n", answer);
	return 0;
}