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 gf(int x,int y)
{
 int tmp,r;
 if(x<y){tmp=x;x=y;y=tmp;} 
  r=x%y;
 if(r==0)
 {return y;}
 if(r!=0)
 {return gf(y,r);}
}
 
int main(void)
{
 int N,M;
 unsigned int L;
  scanf("%d %d",&N,&M); 
 char S[N],T[M];
  scanf("%s",S);
  scanf("%s",T);
  L=N*M/gf(N,M);
 int k,flag,dS,dT;
   flag=0;
   dS=L/N;
   dT=L/M;
 
   for(k=0;k<N;k++)
   {
     if((k*dS)%dT==0)
     {
      if(S[k]!=T[k*dS/dT]){
        flag=1;
        break;}
     }
   } 
 
 if(flag==1){printf("-1");}
 if(flag==0){printf("%d",L);}
 return 0;
}