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: Wrong Answer)

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
long gcd(long x, long y);
int main(void){
  long n,m,i,x,y,g=0;
  scanf("%ld %ld", &n, &m);
  if(n<m){
    i=n;
    n=m;
    m=i;
    g=1;
  }
  char s[n], t[m];
  if(g==1){
   scanf("%s", t);
   scanf("%s",s);
  }
  else {
   scanf("%s", s);
   scanf("%s", t);
  }
  g = gcd(n,m);
  x = n/g;
  y = m/g;
  for(i=0; ((m >= y*i) && (n >= x*i)); i++){
     
    if(*(s+x*i)==*(t+y*i)); 
    else{
     x=1;
     y=1;
     g=-1;
     break;
     }
   }
  printf("%ld",x*y*g);
  return 0;
}
long gcd(long x, long y){
	return y==0 ? x:gcd(y,x % y);
}