iPython widgets: interact() with html result

I've recently discovered iPython widgets, and I would like to use them to provide more intearction for users. In particular, I have a function that returns an HTML table, based on choices made by user.

When I use the widgets and interact, the HTML table does not get updated. Instead, each time the user makes a selection, it prints a new table below, and it's not very helpful since the tables can be quite large.

On the other hand, if I return the string only of the HTML table, it is updated, but again not very helpful for visualization!

Is there any solution for the HTML table to be updated instead of printed each time the user makes a selection?

EDIT: Nevermind, I found out how to link the html output to another widget!

Here is an example of working code, with a simple table:

from IPython.display import display,HTML
#ipywidgets imports
from __future__ import print_function
from ipywidgets import *
import ipywidgets as widgets

#EDIT
#added an html widget for output
w3 = widgets.HTML(value="")

def my_function(a, b):
    html_table = '<table><thead>'
    for col in a:
        html_table += '<th>'+col+'</th>'
    html_table += '</thead><tbody>'
    for row in b:
        html_table += '<tr>'
        for col in a:
            html_table += '<td>'+row+'</td>'
        html_table += '</tr>'
    html_table += '</tbody></table>'

    #EDIT
    w3.value = html_table
    #return HTML(html_table)
    #return html_table

widget1 = widgets.SelectMultiple(
    description="columns:",
    options=['A', 'B', 'C', 'D', 'E', 'F', 'G']
)

widget2 = widgets.SelectMultiple(
    description="rows:",
    options=['A', 'B', 'C', 'D', 'E', 'F', 'G']
)

#EDIT
interact(my_function, a=widget1, b=widget2)
display(w3)