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 Pascal (FPC 2.6.2) (judge verdict: Time Limit Exceeded)

var
  a,b,c:string;
  t:char;
  n,m,i,j,p,q,k:longint;
function gcd(a,b:longint):longint;
begin
  if b=0 then exit(a)
  else exit(gcd(b,a mod b));
end;
begin
  readln(n,m);
  readln(a);
  readln(b);
  if n>m then i:=n
  else i:=m;
  k:=gcd(i,n+m-i);
  p:=k div n;
  q:=k div m;
  i:=1;
  j:=1;
  while (j<=m)and(i<=n) do
  begin
	 if b[j]<>a[i] then begin writeln('-1'); halt; end;
     i:=i+q;
	 j:=j+p;
  end;
  writeln(k);
end.