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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h>

int gcd(int a, int b) {return !b?a:gcd(b,a%b);}
int lcm(int a, int b) {return a/gcd(a,b)*b;}

int main() {
    char s[200000],t[200000];
    int n,m,sw=0,l,sidx=0,tidx=0;
    scanf("%d %d %s %s",&n,&m,s,t);
    l=lcm(n,m);
    while(sidx<n && tidx<m) {
        if(s[sidx]!=t[tidx]) {sw=1; break;}
        sidx+=l/m;
        tidx+=l/n;
    }
    if(sw) printf("%d",-1);
    else printf("%d",l);
    return 0;
}