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public class LoginServlet extends HttpServlet {
    private static final long serialVersionUID = 1L;

    private final String username = "admin";
    private final String password = "password";

    protected void doPost(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {

        //Obtener las variables de la vista
        String username = request.getParameter("username");
        String password = request.getParameter("pwd");


        if (this.username.equals(username) && this.password.equals(password)) {
            //Verificamos si existe una sesión anterior
            HttpSession oldSession = request.getSession(false);
            if (oldSession != null) {
                oldSession.invalidate();
            }
            //Creamos una nueva sesión
            HttpSession newSession = request.getSession(true);

            //Configuración de la sesión a expirar en 5 minutos
            newSession.setMaxInactiveInterval(5*60);

            //Creación del Cookie
            Cookie message = new Cookie("message", "Welcome");
            message.setHttpOnly(true);
            message.setSecure(true);
            response.addCookie(message);
            response.sendRedirect("admin/loginSuccess.jsp");
        } else {
            //Se direcciona a la pagina del login
            RequestDispatcher rd = getServletContext().getRequestDispatcher("/loginPage.jsp");
            PrintWriter out = response.getWriter();
            out.println("<font color=red>Either username or password is wrong.</font>");
            rd.include(request, response);
        }
    }

}

public class LogoutServlet extends HttpServlet {
    private static final long serialVersionUID = 1L;

    protected void doPost(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {

        //Invalidar la sesión si existe
        HttpSession session = request.getSession(false);

        if(session!=null) {
            session.invalidate();
        }
        response.sendRedirect(request.getContextPath()+"/loginPage.jsp");
    }

}

<%@ page language="java" contentType="text/html; charset=ISO-8859-1"
    pageEncoding="ISO-8859-1"%>
<!DOCTYPE html>
<html>
<head>
<meta charset="ISO-8859-1">
<title>Login Success Page</title>
</head>
<body>
    <%
        String message = null;
        String sessionID = null;

        Cookie[] cookies = request.getCookies();
        if (cookies != null) {
            for (Cookie cookie : cookies) {
                if (cookie.getName().equals("message"))
                    message = cookie.getValue()+ " " + cookie.getSecure();
                if (cookie.getName().equals("JSESSIONID"))
                    sessionID = cookie.getValue();
            }
        }
    %>

    <h3>Login Success</h3>
    <h4><%=message%></h4>
    <h4>
        Session ID =
        <%=sessionID%></h4>
    <br>
    <br>
    <form action="LogoutServlet" method="post">
        <input type="submit" value="Logout">
    </form>
</body>
</html>

<!DOCTYPE html>
<html>
<head>
    <meta charset="UTF-8">
    <title>Login Page</title>
    <h1>Please login to continue</h1>
</head>
<body>
<form action="LoginServlet" method="post">

    Username: <input type="text" name="username">
    <br>
    Password: <input type="password" name="pwd">
    <br><br>
    <input type="submit" value="Login">
</form>
</body>
</html>