Integrate easing on mouse wheel with arrows

I use this script to "fix" the problem of IE and Chrome not having a continous smooth scroll when using mouse wheel:

if (window.addEventListener) window.addEventListener('DOMMouseScroll', wheel, false);
window.onmousewheel = document.onmousewheel = wheel;

function wheel(event) {
    var delta = 0;
    if (event.wheelDelta) delta = event.wheelDelta / 120;
    else if (event.detail) delta = -event.detail / 3;

    handle(delta);
    if (event.preventDefault) event.preventDefault();
    event.returnValue = false;
}

function handle(delta) {
    var time = 1000;
    var distance = 260;

    $('html, body').stop().animate({
        scrollTop: $(window).scrollTop() - (distance * delta)
    }, time );
}

(JSFIDDLE)

What I'd like to have is integrate also the arrow keys in this. How do I rewrite this script adding the eventListener of arrow keys "scrolling" and applying the easing?

Living demo: http://jsfiddle.net/cZuym/39/

You just have to play with the keydown event and the animation of the scroll. Note that now the variables time and distance are globals:

if (window.addEventListener) window.addEventListener('DOMMouseScroll', wheel, false);
window.onmousewheel = document.onmousewheel = wheel;

var time = 1000;
var distance = 300;

function wheel(event) {
    if (event.wheelDelta) delta = event.wheelDelta / 120;
    else if (event.detail) delta = -event.detail / 3;

    handle();
    if (event.preventDefault) event.preventDefault();
    event.returnValue = false;
}

function handle() {

    $('html, body').stop().animate({
        scrollTop: $(window).scrollTop() - (distance * delta)
    }, time);
}


$(document).keydown(function (e) {

    switch (e.which) {
        //up
        case 38:
            $('html, body').stop().animate({
                scrollTop: $(window).scrollTop() - distance
            }, time);
            break;

            //down
        case 40:
            $('html, body').stop().animate({
                scrollTop: $(window).scrollTop() + distance
            }, time);
            break;
    }
});