<?php if(!isset($s)) $s = 'Search Xmas';?>
<div>
<form method="get" id="searchform" action="<?php home_url('/') ; ?>">
<input class="text" type="text" value="<?php if(trim(esc_html($s,1))!='') echo trim(esc_html($s,1));else echo ' ';?>" name="s" id="s" />
<input type="submit" class="submit" name="Submit" value="Search!" />
</form>