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 5.4.1) (judge verdict: Runtime Error)

#include<stdio.h>
int main()
{
    int n, m;
    scanf("%d %d", &n, &m);
    char s[100005], t[100005];
    scanf("%s%s", s, t);
    int a = n, b = m, r = n % m;
    while (r > 0)
    {
        a = b;
        b = r;
        r = a % b;
    }
    if (b == 1)
        printf("%d\n", n*m);
    else
    {
        int i;
        char x[200005] = {};
        a = n * m / b;
        for (i = 0; i < n; i++)
        {
            x[i*a / n] = s[i];
        }
        for (i = 0; i < m; i++)
        {
            if (x[i*a / m] != 0 && x[i*a / m] != t[i])
            {
                printf("-1\n");
                return 0;
            }
        }
        printf("%d\n", a);
    }
    return 0;
}