Integer divison using bitwise operators

HTML

<h1>Integer divison using bitwise operators</h1>

<div>
    <label for="a">Divisor <i>a</i> =</label>
    <input type="text" id="a" value="3" />
</div>
<div>
    <label for="m">Dividend <i>n</i> &lt; 2<sup><i>m</i></sup>, where exponent <i>m</i> =</label>
    <select id="m">
        <option>1</option>
        <option>2</option>
        <option>3</option>
        <option>4</option>
        <option>5</option>
        <option>6</option>
        <option selected>7</option>
        <option>8</option>
        <option>9</option>
        <option>10</option>
        <option>11</option>
        <option>12</option>
        <option>13</option>
        <option>14</option>
        <option>15</option>
        <option>16</option>
        <option>17</option>
        <option>18</option>
        <option>19</option>
        <option>20</option>
        <option>21</option>
        <option>22</option>
        <option>23</option>
        <option>24</option>
        <option>25</option>
        <option>26</option>
        <option>27</option>
        <option>28</option>
        <option>29</option>
        <option>30</option>
        <option>31</option>
        <option>32</option>
    </select>
</div>
<div>
    <input type="button" id="generate" value="Generate formula" />
</div>
<div>Formula: <span id="formula">---</span>

</div>

CSS

* {
    margin: 0;
    padding: 0;
    font:"Times" 1em;
}
h1, div {
    margin: 10px;
}
input[type="button"] {
    padding: 5px;
}
input[type="text"], select {
    width: 50px;
}

JavaScript

var $a = $("#a"),
    $m = $("#m"),
    $generate = $("#generate"),
    $formula = $("#formula");

$generate.click(function () {
    var a = +$a.val(),
        m = +$m.val(),
        m2 = 0,
        k = 0;

    if (isNaN(a) || a !== Math.floor(a) || a < 2 || a > Math.pow(2, 31) - 1) {
        alert("Divisor \"a\" must be an integer between 2 and 2^32-1");
        return;
    }
    m2 = Math.pow(2, m);
    k = Math.ceil(m2 / a);
    $formula.html("<i>n</i> / " + a + " = (" + k + " * <i>n</i>) &gt;&gt; " + m + "; for all <i>n</i> &lt; " + m2);
});

$generate.click();