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 <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <limits.h>
char lowcmp[26]="abcdefghijklmnopqrstuvwxyz";
char upcmp[26]="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
long long mod=1000000007;
int max(int a, int b){return a>b?a:b;}
int min(int a, int b){return a<b?a:b;}
int gcd(int a, int b){return min(a,b)==0?max(a,b):gcd(min(a,b),max(a,b)%min(a,b));}
long long llmax(long long a, long long b){return a>b?a:b;}
long long llmin(long long a, long long b){return a<b?a:b;}
long long llgcd(long long a, long long b){return min(a,b)==0 ?llmax(a,b):llgcd(llmin(a,b),llmax(a,b)%llmin(a,b));}
int assort(const void *a, const void *b){return *(int*)a-*(int*)b;}
int dessort(const void *a, const void *b){return *(int*)b-*(int*)a;}
int llassort(const void *a, const void *b){return *(long long*)a-*(long long*)b;}
int lldessort(const void *a, const void *b){return *(long long*)b-*(long long*)a;}
int charassort(const void *a, const void *b){return strcmp((char*)a ,(char*)b);}
int chardessort(const void *a, const void *b){return strcmp((char*)b ,(char*)a);}
int ntoi(char c){return c-'0';}
int ltoi(char c){return c-'a';}
int utoi(char c){return c-'A';}
long long ncr(int a,int b){long long ans=1;for(int i=0;i<b;i++){ans=ans*(a-i)/(i+1);}return(ans);}
long long npr(int a,int b){long long ans=1;for(int i=0;i<b;i++){ans=ans*(a-i);}return(ans);}


int main(void){
    int n,m,ans;
    scanf("%d%d",&n,&m);
    ans=n*m/gcd(n,m);
    char s[n+3],t[m+3];
    scanf("%s%s",s,t);
    for (int i=0; i<gcd(n,m); i++){
        printf("%c %c\n",s[i*ans/m],t[i*ans/n]);
        if (s[i*ans/m]!=t[i*ans/n]){
            ans=-1;
            break;
        }
    }
    printf("%d\n",ans);
	return 0 ;
}