<?php
session_start();
include("passwords.php");
if ($_POST["ac"]=="log") { /// do after login form is submitted
     if ($USERS[$_POST["username"]]==$_POST["password"]) { /// check if submitted username and password exist in $USERS array
          $_SESSION["logged"]=$_POST["username"];
     } else {
          echo 'Incorrect username/password. Please try again.';
     };
};
if (array_key_exists($_SESSION["logged"],$USERS)) { //// check if user is logged or not
     echo "You are logged in."; //// if user is logged show a message
} else { //// if not logged show login form
     echo '<form action="default.php" method="post"><input type="hidden" name="ac" value="log"> ';
     echo 'Username: <input type="text" name="username" />';
     echo 'Password: <input type="password" name="password" />';
     echo '<input type="submit" value="Login" onClick="location.href=\'index.html\'"/>';
     echo '</form>';
};
?>

Error: Notice: Undefined index: ac in C:\xampp\htdocs\default.php on line 4