Jquery: how to prevent key UP & DOWN behavior in HTML Input Fields?

Jquery: how to prevent key UP & DOWN behavior in HTML Input Fields?

I know there are similar questions on stackoverflow, but
none of them I think has working solution :((
So when you type key UP or Down when you have focus on an HTML input field,
the cursor automatically moves to the front/end of the input value.
(You can check this with the Top-right Search box on the stackoverflow site).
I want to remove this!!
I tried the following code, but didn't work:
$(document).on("keydown", "#input_field", function(event) {
if(event.which==38 || event.which==40){
event.preventDefault();
}
});
Any solution for this..?
Thanks!