How can I choose what is blocked when a Modal is opened?

HTML

<script src="//maxcdn.bootstrapcdn.com/bootstrap/3.3.2/js/bootstrap.min.js"></script>
<link rel="stylesheet" href="//maxcdn.bootstrapcdn.com/bootstrap/3.3.2/css/bootstrap.min.css">
<div class='menu'>Your menu <input type='text' /></div>

<!-- Button trigger modal -->

<button type="button" class="btn btn-primary btn-lg" data-toggle="modal" data-target="#myModal">
  Launch demo modal
</button>

<!-- Modal -->
<div class="modal fade" id="myModal" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true">
  <div class="modal-dialog">
    <div class="modal-content">
      <div class="modal-header">
        <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">&times;</span></button>
        <h4 class="modal-title" id="myModalLabel">Modal title</h4>
      </div>
      <div class="modal-body">
        ...
      </div>
      <div class="modal-footer">
        <button type="button" class="btn btn-default" data-dismiss="modal">Close</button>
        <button type="button" class="btn btn-primary">Save changes</button>
      </div>
    </div>
  </div>
</div>

CSS

.menu {
    border: 1px solid grey;
    margin: 10px 20px;
    background: #fff;
    text-align : center;
    z-index: 1041;
    position: relative;
}