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: Runtime Error)

var
  a,b,c:string;
  t:char;
  n,m,i,j,p,q,k:longint;
begin
  readln(n,m);
  readln(a);
  readln(b);
  p:=n;
  q:=m;
  if p<q then begin i:=p; p:=q; q:=i; end;
  while (p mod q)<>0 do if p>q then begin p:=p mod q; i:=p; p:=q; q:=i; end;
  k:=n*m div q;
  i:=1;
  t:='2';
  while true do
  begin
    t:='2';
    i:=i+q;
    if i>k then break;
    if ((i-1) mod (k mod n)=0) then 
    begin
      c[i div q]:=a[(i-1) div (k mod n)+1];
      if ((i-1) mod (k mod m)=0) then t:=b[(i-1) div (k mod m)+1];
      if (t<>'2')and(t=c[i]) then continue
      else if (t<>'2') then begin writeln('-1'); halt; end;
    end;
  end;
  writeln(k);
end.