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: Accepted)

var
	i:Longint;
	n,m,u:int64;
	s,t:String;
function gcd(a,b:int64):int64;
begin
	if b=0 then gcd:=a else gcd:=gcd(b,a mod b);
end;
begin
	readln(n,m);
	setlength(s,n);
	setlength(t,m);
	readln(s);
	readln(t);
	u:=gcd(n,m);
	for i:=0 to u-1 do if s[n div u*i+1]<>t[m div u*i+1]then begin
		writeln(-1);
		exit;
	end;
	writeln(n*m div u);
end.