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: Wrong Answer)

var
	n,m,t1,i:longint;
	s,t,t2:ansistring;
function gcd(x,y:longint):longint;
var
	t,r:longint;
begin
	if x<y then
	begin
		t:=x; x:=y; y:=t;
	end;
	r:=x mod y;
	while r<>0 do
	begin
		x:=y; y:=r;
		r:=x mod y;
	end;
	exit(y);
end;
begin
	readln(n,m);
	readln(s); readln(t);
	if n<m then
	begin
		t1:=n; n:=m; m:=t1;
		t2:=s; s:=t; t:=t2;
	end;
	if n mod m=0 then 
	begin 
		for i:=0 to m-1 do
			if i*n div m+1<>i+1 then
			begin
				writeln(-1);
				exit;
			end;
		writeln(n);
	end
	else writeln(n*m div gcd(n,m));
end.