want to show table on ajax based page using servlet

I want to display the table on my page using servlet, i have used servlet to create AJAX, the problem is the Table is not printing on the page for the suggestion, i want to make it

My code is for the

home.jsp

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
"http://www.w3.org/TR/html4/loose.dtd">
<%@ page contentType="text/html;charset=windows-1252"%>
<%@ taglib uri="http://java.sun.com/jsf/core" prefix="f"%>
<%@ taglib uri="http://java.sun.com/jsf/html" prefix="h"%>
<f:view>
  <html>
    <head>
    <script type="text/javascript">
     function doSuggest(word)
    {
      if(word.length > 0) {
         alert("Within doSuggest"+word);
          var request = null;
          if(window.XMLHttpRequest)
          {
              alert(" xml Object instantiated");
              request = new XmlHttpRequest();
              alert(" xml Object Created");
          } 
          else if (window.ActiveXObject)
          {
          request = new ActiveXObject("Microsoft.XMLHTTP");
          }
          if(request)
          {
//          var contextPath = document.getElementById("frmHome:path");
//          alert(contextPath);
//          var url= contextPath; 
          var url ="http://localhost:8080/ajaxjsf/hintservlet";
          url+="?key="+word;
          
          alert("url created"+url);
          request.open("POST",url);
          request.onreadystatechange = function()
          {
           if(request.readystate == 4)
           { 
            alert("In ready state ");
            document.getElementById("frmHome:dtHint").innerHTML=request.responseText;
            document.getElementById("frmHome:dtHint").style.visibility="visible";

}
         }
             request.send(null);
            
          }
          else
          {
           alert("Your browser don't support AJax !"); 
          }
          
          }
          else
          {
            document.getElementById("frmHome:dtHint").innerHTML="";
            document.getElementById("frmHome:dtHint").style.visibility="hidden";

}
    }
    
    </script>
    
      <meta http-equiv="Content-Type"
            content="text/html; charset=windows-1252"/>
      <title>home</title>
    </head>
    <body>
      <h:form  id="frmHome">
      <h:outputText value="Enter Name"/>
      
        <h:inputText id="inputtxtUser" onkeyup="doSuggest(this.value)"/>
        <h:dataTable id="dtHint"
                     style="width:22em;border:1px black solid;padding-left:2px;padding-right:2px; visibility: hidden"/>
      </h:form>
    </body>
  </html>
</f:view>
<%-- oracle-jdev-comment:auto-binding-backing-bean-name:backing_home--%>

and Servlet is

package ajaxjsf.web.hintservlet.servlet;

import java.io.IOException;
import java.io.PrintWriter;

import java.util.ArrayList;
import java.util.List;

import javax.servlet.*;
import javax.servlet.http.*;

public class HintServlet extends HttpServlet {
    private static final String CONTENT_TYPE = "text/html; charset=windows-1252";

public void init(ServletConfig config) throws ServletException {
        System.out.println("With in Servlet");
        super.init(config);
        System.out.println("With in Servlet");
    }

public void doGet(HttpServletRequest request, 
                      HttpServletResponse response) throws ServletException, 
                                                           IOException {
//        
//         response.setContentType(CONTENT_TYPE);
//         //response.setContentType("text/html");
//         PrintWriter out = response.getWriter();        
//         String suggetsword=request.getParameter("key").toLowerCase(); 
//         System.out.println("Key has got"+suggetsword);
//         List matches = getMatches(suggetsword);
//         System.out.println("Matches sizs ? "+matches.size());
//         out.println("<table width='100%' border='0' cellpadding='0' cellspacing='0'>");
//         for(Object match:matches){
//             System.out.println("match:"+match);
//            out.print("<tr><td>"+match+"</td></tr>");
//         }
//         out.println("</table>");
//        
//        out.flush();
//        out.close();

}

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

response.setContentType(CONTENT_TYPE);
        //response.setContentType("text/html");
        PrintWriter out = response.getWriter();        
        String suggetsword=request.getParameter("key").toLowerCase(); 
        System.out.println("Key has got"+suggetsword);
        //List matches = getMatches(suggetsword);
        List<String> mySuggests=new ArrayList<String>();
        mySuggests.add("Anna");
        mySuggests.add("Apple");
        mySuggests.add("America");
        mySuggests.add("Ball");
        mySuggests.add("Brittany");
        mySuggests.add("Cinderella");
        mySuggests.add("Car");
        mySuggests.add("Diana");
        mySuggests.add("Eva");
        mySuggests.add("Ear");
        mySuggests.add("Fiona");
        mySuggests.add("Fan");
        mySuggests.add("Gunda");
        mySuggests.add("Game");
        mySuggests.add("mno");
        mySuggests.add("pqr");
        System.out.println("Matches sizs ? "+mySuggests.size());
        out.println("<table width='100%' border='1' cellpadding='0' cellspacing='0'>");
        for(String match:mySuggests)
        //for(int match= 0; match<mySuggests.size(); match++)
        {
           System.out.println("match:"+match);
           //out.print("<tr><td>"+match+"</td></tr>");
            out.print("<tr>");
            out.print("<td>"+match+"</td>");
            out.print("</tr>");
        }
        out.println("</table>");
              
        out.close();
        
        
    }

public void doPut(HttpServletRequest request, 
                      HttpServletResponse response) throws ServletException, 
                                                           IOException {
      
    }
    
  public List getMatches(String key )
  {
      System.out.println("With in getMatches()");
          List<String> mySuggests=new ArrayList<String>();
          mySuggests.add("Anna");
          mySuggests.add("Apple");
          mySuggests.add("America");
          mySuggests.add("Ball");
          mySuggests.add("Brittany");
          mySuggests.add("Cinderella");
          mySuggests.add("Car");
          mySuggests.add("Diana");
          mySuggests.add("Eva");
          mySuggests.add("Ear");
          mySuggests.add("Fiona");
          mySuggests.add("Fan");
          mySuggests.add("Gunda");
          mySuggests.add("Game");
          mySuggests.add("mno");
          mySuggests.add("pqr");
          return mySuggests;
         
      
      
      
      }
 
    
    
    
    
}