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>
long long gcd(long long a,long long b){return b?gcd(b,a%b):a;}
long long lcm(long long a,long long b){return a*(b/gcd(a,b));}
long long 
int main(){
  long long n,m,a,i;
  char s[100010],t[100010];
  scanf("%lld %lld",&n,&m);
  scanf("%s %s",s,t);
  a=lcm(n,m);
  if(s[0]-t[0])a=-1;
  if(n%m==0){
    for(i=0;i<m;i++){
      if(s[i*n/m]-t[i])a=-1;
    }
  }
  if(m%n==0){
    for(i=0;i<n;i++){
      if(t[i*m/n]-t[i])a=-1;
    }
  }
  printf("%lld\n",a);
  return 0;
}